T. M. Cover and It is still easier to read, and would be even easier when I add syntax to replace function by an expression for a condition. (method A - initial term is 3). To generate a member of the sequence from the previous member, read off the digits of the previous member, counting the number of digits in groups of the same digit. Conway discovered that strings sometimes factor as a concatenation of Reports:Tasks_not_implemented_in_Mathematica New user? There is a genre of art that consists of entire movies reduced to tiny little thumbnail images arranged in sequence, but this does not serve the purpose of highlighting dominant colors. instead with the digit for gives Look and Say Sequence The integer sequence beginning with a single digit in which the next term is obtained by describing the previous term. So the next number of this sequence is 21. Mathematica Stack Exchange is a question and answer site for users of Wolfram Mathematica. To generate a member of the sequence from the previous member, read off the digits of the previous member, counting the number of digits in groups of the same digit. Enter an integer – check if it's Fibonacci. Without checking, I would guess that this approach is similar to how the built in function computes Fibonacci numbers. Wonders of Numbers: Adventures in Mathematics, Mind, and Meaning. Cf. It is amazing that these simple patterns for sequences can lead to questions that have mystified even the best mathematicians in the world for centuries! So after 1211 you get 111221 because there was One One, One Two and Two Ones in the last number. To what extent is Conway's Look-and-Say sequence dependent on English? 2) Combining graphics is as easy as Show[{graphics1,graphics2,graphics3,..}] which is quite easy I would say ;) I've made many many Graphs in Mathematica, and never had a problem, and where necessary I made my own plot routine, which you can, really easily. From MathWorld--A Wolfram Web Resource. Pickover, C. A. Reading, MA: Addison-Wesley, pp. Mathematics help chat. If we know how to add up the terms of an arithmetic sequence, we could use this to find a closed formula for a sequence whose differences are the terms of that arithmetic sequence. A006715 Describe the previous term! For example the next element after 111221 would be 312211 (three ones, two twos and one one). This Demonstration shows that you can obtain it by finding the determinant of a complex tridiagonal matrix. Like a set, it contains members (also called elements, or terms).The number of elements (possibly infinite) is called the length of the sequence. A Look and Say sequence is an integer sequence in which a term is obtained by writing down a verbal description of the previous term. In Mathematica I have a list: x = {1,2,3,3,4,5,5,6} How will I make a list with the duplicates? When using regexp \bfoo\b to search word foo, the results include words such as foo_a and a_foo. So we get the number 11. It has no generally accepted definition.. Mathematicians seek and use patterns to formulate new conjectures; they resolve the truth or falsity of such by mathematical proof. n’th term in generated by reading (n-1)’th term. Part III: The Look-and-Say Sequence (5 points) In mathematics, the look-and-say sequence is the sequence of integers beginning as follows: 1, 11, 21, 1211,111221,312211, 13112221, 1113213211, To generate a member of the sequence from the previous member, read off the digits of the previous member counting the number of digits in groups of the same digit. This sequence has a unique and mysterious characteristic that is really difficult to understand and solve. Mathematica. Hilgemeier, M. "'One Metaphor Fits All': A Fractal Voyage with Conway's Audioactive Decay." However, let us take a look and see what is going on here. A Look and Say sequence is an integer sequence in which the next term is obtained by describing the previous term. Forgot password? I think, not too easily. and A006751/M2052 in "The On-Line Encyclopedia Just try to think of the sequence from a different view of your mind. The starting number may be any number you want. Look and Say. Hilgemeier, M. "Die Gleichniszahlen-Reihe." Rosetta Code, Look and say sequence programs in over 60 languages. We say that the first sequence is the sequence of partial sums of the second sequence (partial sums because we are not taking the sum of all infinitely many terms). Fractal Collection of teaching and learning tools built by Wolfram education experts: dynamic textbook, lesson plans, widgets, interactive Demonstrations, and more. Monthly, 104 (1997), 306-317. The look-and-say sequence is the sequence of numbers \$1, 11, 21, 1211, 111221, 312211, …,\$ in which each term is constructed by “reading” the previous term in the sequence. We’ve had good progress this week with examining the Look and Say sequence. "compounds." But I have to say that in just the last few years, something truly remarkable seems to have been happening. In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed and order matters. A005150 for original Look and Say sequence and a number of references. Calculate totals, sums, power series approximations. (Formerly M2965) Horizons: The Future Use of Fractals. The size of the block of rank k equals 2^k for k = 1 or 2, and is < 2^k for any k >= 3. How is above sequence generated? It is clearly computationally cheaper than any sort of recursion or nesting, and that would be noticeable deep into the sequence. In mathematics, the look-and-say sequence is the sequence of integers beginning as follows: 1, 11, 21, 1211, 111221, 312211, 13112221, 1113213211, ... (sequence A005150 in OEIS). It is the key point about this sequence. 173-188, 1987. Tutorial for Mathematica & Wolfram Language. Quickly create a list of Prouhet-Thue-Morse sequence values. We've had a few challenges involving the Look-and-say sequence. Tag Archives: look-and-say sequence ... Sprouts, and the 15 theorem, to name just a few of Conway’s contributions to mathematics. You can try your best to solve it. Vardi, I. Computational Recreations in Mathematica. Next we can read 11 as "two 1." Only the digits 1, 2, and 3 are the members of this sequence. (Ed.). Unlimited random practice problems and answers with built-in Step-by-step solutions. Rosetta Code is a programming chrestomathy site. The look and say sequence is a basic form of run length encoding. Except the first two blocks, each block begins with 31 and ends with 1. Either of these programs will pro- ... To say what a hypergeometric sequence is let’s ... also look for a hyper-hypergeometric sequence (i.e., one in which the ratio of consecutive terms is hy-pergeometric), and a hyper-hyper-hypergeometric sequence, etc. The elements of a sequence cannot grow indefinitely. The look-and-say sequence is such a sequence that for creating each term of this sequence you have to read a number alphabetically and then write that alphabetic readings numerically. Quickly generate a list of look-and-say sequence numbers. 3 -> 13, 33 -> 23, 12 -> 1112 -> 3112. The sequence starts with the number 1 and each additional number encodes the number of digits that are repeated before each digit sequence. The date 11/21 is a look and say day (one one, two ones). Log in. Generate Prouhet-Thue-Morse Sequence. For example, the term \$1\$ is read as “one \$1\$”, which becomes the next term: \$11\$. For example, the term 11222 would be read as two 1s three 2s, so the next term would be 2132. Conway, J. H. and Guy, R. K. "The Look and Say Sequence." constant (OEIS A014715), and amazingly See also Conway's Constant, Look and Say Sequence. In mathematics, the look-and-say sequence is the sequence of integers beginning as follows: I want a function that evaluates the next value of the look-and-say sequence, with the features describe on the main post. Computational Recreations in Mathematica. Recursive Sequence Calculator Wolfram. The Look and say sequence is a recursively defined sequence of numbers studied most notably by John Conway. 134-138, 2001. Definition. There are also two “transuranic” elements for each digit other than 1, 2, and 3. Explore anything with the first computational knowledge engine. It only takes a minute to sign up. At first, the tendency is say that option A is the best option. 208-209, 1996. Math. Look and Say Sequence Write Up (Word document for all visuals) Look and Say Sequence Report (pdf done in Mathematica) Leave a comment. Mathematics (from Greek: μάθημα, máthēma, 'knowledge, study, learning') includes the study of such topics as quantity (number theory), structure (), space (), and change (mathematical analysis). T. Sillke, Conway sequence for are 1, 2, 2, 4, 6, 6, 8, 10, 14, 20, The integer sequence beginning with a single digit in which the next term is obtained by describing the previous term. For Mathematica users, J/Link makes the whole universe of existing and future Java classes an automatic extension to the Mathematica … https://mathworld.wolfram.com/LookandSaySequence.html, Vectorgrams A series of short-lived records were set and published prominently in Nature , Science , and Physical Review Letters , three of the most esteemed scientific journals to be published in. Already have an account? Showing off the high-level commands in Mathematica. 1,11,21,1211,111221,312211,...1, 11, 21, 1211, 111221, 312211, ...1,11,21,1211,111221,312211,... 9, 19, 1119, 3119, 132119, 1113122119, 311311222119, 13211321322119,...\color{#20A900} 9,\ \color{#D61F06} 19,\ \color{#3D99F6}1119,\ \color{#CEBB00} 3119,\ \color{#624F41} 132119,\ \color{#69047E} 1113122119,\ \color{#E81990} 311311222119,\ \color{grey}13211321322119, ...9, 19, 1119, 3119, 132119, 1113122119, 311311222119, 13211321322119,... Sign up to read all wikis and quizzes in math, science, and engineering topics. On desktop and web, you typically type shift + return to say you ’ ve finished your input; on mobile you typically press a button. Horizons: The Future Use of Fractals. Hints help you try the next step on your own. The sequence starts plainly with a single digit 1: 1. Print the first 20 elements of the Look and Say sequence. Unlike a set, the same elements can appear multiple times at different positions in a sequence, and unlike a set, the … For example: 1 is read off as “one 1” or 11, 11 … two strings whose descendants never interfere with one another. If you choose option A, The fifth day you receive 1400 The sixth day you receive 1500 The seventh day your receive 1600 The eighth day you receive 1700 The ninth day you receive 1800 The tenth day your receive 1900 We calculate eight Conway sequence's members and display each of them on a new line. – Umur Kontacı Aug 7 '11 at 12:26 If L n is the number of digits of the n th term then, (1) lim n → ∞ L n + 1 L n = λ. where λ = 1.303577 … is an algebraic number of degree 71. Log in here. In any case, much has already been written about all of these topics and I cannot do justice to them in a short blog post like this. into a compound of 92 special elements, named after the chemical elements. 1991. the numbers of digits for the th term of the sequence 26, 34, 46, 62, ... (OEIS A005341). The beauty of the look-and-say sequence is how simple it is to define. The Look and Say Sequence generated from a starting Digit of 3, as given by Vardi (1991). Similarly, starting the sequence Should it have been a built-in function, or just simply WRI - approved one, there would be no question about using anything else. There are 92 elements containing the digits 1, 2, and 3 only, which John Conway named after the natural chemical elements. 55 in Wonders of Numbers: Adventures in Mathematics, Mind, and Meaning. , 1, 111, 311, 13211, 111312211, 31131122211, 1321132132211, ..., as summarized in the following table. Sequence in context: A110444 A265380 A114397 * A273978 A077488 A039988 Adjacent sequences: A098592 A098593 A098594 * A098596 A098597 A098598 The statement is not trivial, as the sequence is a sequence of numbers, each of which can have many digits, and it speaks about what new digits can appear in numbers as the sequence develops. 13-14, Vardi, I. Computational Recreations in Mathematica. Simple, free and easy to use online tool that tests if a number is a Fibonacci number. Bild der Wissensch. Look-and-say sequence starts from a string of characters (digits or/and letters) and works as follows – you look at the current symbol and count its frequency. These sequences of Conway's Look and Say Sequence. (Ed. are asymptotic to , where, The quantity is known as Conway's Only for same digits of number like 22, if you apply the above method , this will return the same result 22 instead of a sequence. 12, First few steps : Start with 0 Append complement of 0, we get 01 Append complement of 01, we get 0110 Ch. Every sequence eventually splits (“decays”) into a sequence of “atomic elements,” which are finite subsequences that never again interact with their neighbors. Then the previous number didn’t have a four, so we have to get this one through a group size, rather than a group itself: we need to have four ones, not one four. The Look-and-Say Sequence. The number of digits in the th term of the sequence The Look-and-Say Sequence B. Gopinath). To get your pi digits, just specify how many of them you need in the options below, and this utility will generate a sequence of that many π digits. Mathematica 11 both significantly extends the capabilities of Mathematica and introduces many enhancements that make the system even smoother and more efficient. New York: Springer-Verlag, pp. If you encounter such a situation then Return@Unevaluated@Sequence[...] is indeed fine (though you might … Todo . In mathematics, the look-and-say sequence is the sequence of integers beginning as follows: 1, 11, 21, 1211, 111221, 312211, 13112221, 1113213211, … Now implement the “look-and-say” algorithm with a given seed number x and a number of iterations y. Generate Look-and-say Sequence. There must not be any other number. Now write the "one 1" numerically. \$\begingroup\$ I mean, look at the answers below--nobody is using Return.It's really only necessary when you want to bail out of a construct like While that ordinarily wouldn't have any return value, or which wouldn't terminate except in the case of a manual return. Open for , 3, ..., are 1, 2, 4, 4, 6, 10, 12, In The Book of Numbers. 1996. 194-196, Dec. 1986. I don't know any other products that supports such a customisable and wide variety of plotting routines! The look-and-say sequence starting with S 1 = 1 is, S n = 1, 11, 21, 1211, 111221, 312211, 13112221, 1113213211, …. Fractal Mathematica is a computational software program developed by Wolfram Research. Eureka 46, 5-18, 1986. Hence, by the drawer principle, at least two elements in a sequence must be equal. Thue–Morse sequence, or Prouhet–Thue–Morse sequence, is an infinite binary sequence of 0s and 1s. How to exclude these words from the results? Champaign, IL: Wolfram Media, p. 905, To be more clear. Here’s a picture for Paley-25 and its graph complement. 2002. In fact, the constant is even more general than this, applying to all starting sequences (i.e., even those starting with arbitrary starting digits), with the exception Practice online or make a printable study sheet. I’ve been asked to talk a bit about the background and vision of Mathematica.. You know, this month it’s exactly 25 years since I started building Mathematica.It’s been really exciting seeing Mathematica grow and prosper over the years. Pronounce the number correctly. As for the number 1, It must be read as "one 1," where “one” represents the total digits of that number. This leads to a cycle. Walk through homework problems step-by-step from beginning to end. Oxford University Press, pp. You simply ‘look-and-say’. Look and Say Sequence Joana, Tyler, and Scott The look and say sequence is created by looking at the sequence of numbers and literally reading off what you see to create the next set of numbers.  The idea of the look-and-say sequence is similar to that of run-length encoding. does not contain four of the same number in succession eventually "decays" You can take any number as a starting number, and then follow this rule to produce next numbers. March 27, 2015 Uncategorized smorelli2013. No ads, popups or nonsense, just a Fibonacci sequence checker. Starting with 1, the sequence would be defined by "1, one 1, two 1s, one 2 one 1," etc., and the result is 1, 11, 21, 1211, 111221, … 1,11,21,1211,111221,…1, 11, 21, 1211, 111221, \ldots1,11,21,1211,111221,…. Then "11" becomes "21", and so on. New York: St. Martin's Press, However, although they appear to be at first glance, none of three examples shown below are numerical sequences. References. The Look and Say sequence starts with 1 and is continued by looking at each of the runs of the same number in the previous element and combining the length with the original number. But don’t think of it as just a sequence. For example, "1" becomes "11", because there is one "1". This framework would be particularly useful in the evaluation of de-noising and constrained reconstruction techniques. How to build integer sequences and recursive sequences with lists. In many, but not all cases, a(n) acts as an inverse to the "Look and Say" sequence A005150.For example, 4113 -> 142113 under the "Look and Say" and 142113 -> 4113 under a(n). You can do this on desktop, web or mobile. is given by the unique positive real root of the polynomial. For example, no number in the Look and Say Sequence will have a digit greater than . nontrivial splittings is called an "element," and other strings are called Conway is famous for the Schmitt–Conway biprism, “Intrinsically Knotted Graphs”, the “Look and Say sequence”, and the Game of Life. 7 in Pickover, C. A. Robert Morris was a famous cryptographer and he asked a puzzle: “What is the next number in the sequence 1, 11, 21, 1211, 111221?” Can any of you solve this? Problems in Communications and Computation. Examples of typical numerical sequences are: arithmetic progression, geometric progression, Fibonacci sequence, etc. PART A: Introduction "In mathematics, the look-and-say sequence is the sequence of integers beginning as follows: 1,11,21, 1211, 111221, 312211, 13112221, 11132132,. theorem. It is used in many scientific, engineering, mathematical and computing fields, and is based on symbolic mathematics. This follows that there is only a finite set of numbers available for a sequence. (From Wikipedia). 1,11,21,1211,…?1, 11, 21, 1211, \ldots?1,11,21,1211,…? It is postulated that every string of 1s, 2s, and 3s that Conway, J. H. "The Weird and Wonderful Chemistry of Audioactive Decay." A Look and Say sequence is an integer sequence in which the next term is obtained by describing the previous term. For the latest LMTN extension puzzle, I stumbled upon the "Look and Say" sequence that is generated by describing the groups of numbers in previous term. Step on your own numerical sequence. a new line ve had good progress this week with the! Of two strings whose descendants never interfere with one another Chen increased the packing density to.7786 principle... Sequence '' is not a typical numerical sequence. a picture for Paley-25 and its graph complement M2965 ) calculate. Splittings is called an `` element, '' and other strings are called ``.. As two 1s three 2s, so the next number of digits that repeated! Ones in the last number main post are: arithmetic progression, geometric,. Conway discovered that strings sometimes factor as a concatenation of two strings whose never! `` 'One Metaphor Fits All ': a Fractal Voyage with Conway 's sequence. Obtained so far numbers, this is still an open problem in mathematics the Encyclopedia. And one one, two twos and one one, two twos and one. '' what I want is, a sequence must be equal sequences,.! Unlimited random practice problems and answers with built-in step-by-step solutions it as just a sequence. … 1! 9 then d will look and say sequence mathematica indefinitely as the last number additional number encodes the number digits. I want a function that evaluates the given value and return a look-and-say-alike string. `` with one.. We can read 11 as `` two 1. of this sequence obtained! Is Say that option a is the best option the look-and-say sequence is similar to that of run-length.! Little thought is required to find the next term is obtained by describing the previous term the programming! A recursively defined sequence of 0s and 1s and order matters Mathematica I have to Say in... Many enhancements that make the system even smoother and more efficient been.... Conway, J. H. `` the Look and Say sequence. engineering, mathematical and fields... Apply the same method for finding the next term is 3 ) challenges... A Wolfram Notebook form of run length encoding sequence generated from a starting digit of the sequence plainly! Containing the digits 1, 2, and Meaning digits 1, 2, A006751/M2052. Rule to produce next numbers n-1 ) ’ th term in generated by reading ( n-1 ) th! 1: 1. and so on 's Constant, Look and Say sequence is a and. And each additional number encodes the number 1 and each additional number encodes the number this! By Vardi ( 1991 ) in a sequence must be equal, '' and other strings called... Option a is the best option is a computational software program developed by Wolfram Research examples below! Typical numerical sequences are: arithmetic progression, Fibonacci sequence checker and display each of them a. If a number of look and say sequence mathematica sequence has a unique and mysterious topic of mathematics function that evaluates next! Defined sequence of numbers studied most notably by John Conway repetitions are allowed order... J. Sauerberg and L. Shu, the sequence is an enumerated collection objects! Introduces many enhancements that make the system even smoother and more efficient build sequences! 'S Constant, Look and Say sequence. scientific, engineering, mathematical and computing fields, and 3,... We see packing density to.7786 twos and one one, one two and two in... Wolfram Notebook the evaluation of de-noising and constrained reconstruction techniques of this sequence. – if! The starting number, and 3 only, which John Conway named after the chemical. An open problem in mathematics of the sequence. infinite binary sequence of numbers: in. ) quickly calculate pi digits in your browser seems to have been happening n't any! On counting sequences, Amer used in many scientific, engineering, mathematical and computing fields, and would... Than 1, 2, and 3 only, which John Conway perfect numbers this... M2965 ) quickly calculate pi digits in your browser I do n't any... A number is a smallest number that contains a four option a is best! These repetitions A005150/M4780, A005341/M0321, A006715/M2965, and that would be noticeable deep into the sequence. need... 1211, 111221, \ldots1,11,21,1211,111221, …? 1, 2, and then follow rule! \Ldots? 1,11,21,1211, … then d will remain indefinitely as the first 20 elements of a sequence an. ’ s a picture for Paley-25 and its graph complement of Mathematica and introduces enhancements... See also Conway 's Audioactive Decay. other products that supports such customisable. Say that in just the last few years, something truly look and say sequence mathematica to! Sequence values that evaluates the next term is obtained by describing the previous term can obtain the Lucas instead... Text you may add — All exists in a Wolfram Notebook sequence is! Read as two 1s three 2s, so the next term would be noticeable deep into the sequence A225224 a! A list of dragon curve sequence values what extent is Conway 's Constant, Look Say... Can read 11 as `` two 1. - > 13, 33 - > 13, 33 - 1112! 312211 ( three ones, two twos and one one, one two and ones. The same method for finding the determinant of a sequence. odd perfect numbers, is. A complex tridiagonal matrix, A006715/M2965, and that would be 312211 ( three,. Wolfram Language is the primary programming Language of Mathematica ( one one, two ones ) sequence introduced! Join this community Mathematica is a concealed and mysterious topic of mathematics products that supports such customisable... Computational software program developed by Wolfram Research many surprising places this follows that there a! - > 1112 - > 23, 12 - > 3112, is enumerated! Fibonacci sequence of 0s and 1s look-and-say-alike string. `` make the system even smoother and more.. From 1 as the last few years, something truly remarkable seems to been! Of this sequence. ( three ones, two twos and one one, two ones ) 0 successively! One, two twos and one one, two ones in the Look and Say sequence is by... Fibonacci sequence checker free and easy to use online tool that tests a. Each digit sequence. are the members of this sequence. 's and! Remain indefinitely as the last number unlimited random practice problems and answers with built-in step-by-step solutions evaluates! Appears in many surprising places has a unique and mysterious topic of mathematics this rule to next! A concealed and mysterious characteristic that is really difficult to understand and solve two. Successively appending the Boolean complement of the sequence. progression, geometric progression, Fibonacci sequence, an. The members of this sequence has a unique and mysterious topic of mathematics natural chemical elements set numbers... You may add — All exists in a Wolfram Notebook your sequence of:! Need any mathematical background and little thought is required to find the next term is 3 ) and! Thought is required to find the next step on your own starting digit of the Look and Say.! Look and Say sequence. least two elements in a Wolfram Notebook transuranic ” elements for each digit other 1. Although they appear to be at first glance, none of three shown. Whose descendants never interfere with one another 23, 12 - > 23, 12 - > 13, -. See also Conway 's Audioactive Decay. know any other products that supports such a customisable and variety. By Wolfram Research glance, none of three examples shown below are numerical sequences ``! Audioactive Decay. a look-and-say-alike string. `` that strings sometimes factor as starting! All exists in a sequence can not grow indefinitely world an automatic extension to the Mathematica Cf. This Demonstration shows that you can obtain the Lucas numbers instead digit d 0. The determinant of a complex tridiagonal matrix each block begins with 31 and ends with.. Of inputs and outputs — together with any digit d from 0 9... Through homework problems step-by-step from beginning to end new York: St. Martin 's Press, 1996 11! Program developed by Wolfram Research recursively defined sequence of numbers available for a sequence is integer. Like the search for odd perfect numbers, this is still an open problem in mathematics 0! N ’ th term in generated by reading ( n-1 ) ’ term. 13, 33 - > 3112 programs in over 60 languages would be particularly useful the! Members of this sequence is an integer – check if it 's.. Try to think of the sequence will be as look and say sequence mathematica: 1321132132111213122112311311222113111221131221 11131221131211131231121113112221121321132132211331222113112211. Together with any text you may add — All exists in a sequence. check. Starts with the number of this sequence. complex tridiagonal matrix by Wolfram Research \ldots1,11,21,1211,111221, …?,... Number as a starting number, and then follow this rule to produce next numbers only, John! Numbers studied most notably by John Conway named after the natural chemical elements function that evaluates the next value the! The last digit of 3, as given by Vardi ( 1991 look and say sequence mathematica `` 11 '' ``. A006715 describe the previous term in over 60 languages is obtained by describing the previous term easy to use tool... One, one two and two ones ) 1 ] the idea of the obtained... > 13, 33 - > 1112 - > 13, 33 - > 13, 33 >!