This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A334055 #18 Sep 11 2020 22:33:51 %S A334055 1,1,1,2,1,1,1,1,3,1,4,10,3,1,1,1,1,3,1,3,7,2,9,3,1,7,3,3,4,-1,3,3,-1, %T A334055 4,1,-1,5,9,-1,-1,7,3,1,2,3,1,5,9,5,-1,3,1,4,3,3,4,-1,3,4,-1,3,1,-1,5, %U A334055 7,-1,3,1,1,-1,2,9,11,3,8,4,10,3,4,-1,-1,3,-1,-1,3,3,-1,8,10 %N A334055 Iteration count (or -1) corresponding to A334054(n). %C A334055 This is the number of iterations for the starting number, containing only digits 1,2 and 3 (see A007932) to reappear in the iterative cycle of its own 'Look and Say' description. %C A334055 See A334054 for further details, a list of the number that do reappear in their iterative cycle, and a proof that the number 233 can never reappear in its cycle. %C A334055 For all 1092 numbers up to six digits long containing digits 1,2,3 there are 397 numbers which reappear in their own iterative cycle, while 695 do not and can be proven never will. %C A334055 In the same range, numbers 121322 and 213223 take 33 cycles before reappearing. The final string in the later case has 49470 digits. See the link file for details of the other numbers. %H A334055 Scott R. Shannon, <a href="/A334055/a334055.txt">Details of all 1092 numbers up to six digits long</a>. %e A334055 The numbers containing only digits 1,2 and 3 are given in A007932. %e A334055 a(1) = 1 as the number 1 take one iteration to reappear: 1->11 which contains '1' as a substring. %e A334055 a(4) = 2 as the number 11 takes two iterations to reappear: 11->21->1211 which contains '11' as a substring. %e A334055 a(9) = 3 as the number 23 takes three iterations to reappear: 23->1213->11121113->31123113 which contains '23' as a substring. %e A334055 a(11) = 4 as the number 32 takes four iterations to reappear: 32->1312->11131112->31133112->1321232112 which contains '32' as a substring. %e A334055 a(12) = 10 as the number 33 takes ten iterations to reappear: 33->23->1213->11121113->31123113->132112132113->11131221121113122113->311311222112311311222113->1321132132211213211321322113->11131221131211132221121113122113121113222113->3113112221131112311332211231131122211311123113322113 which contains '33' as a substring. %Y A334055 Cf. A334054, A005150, A007932, A119566, A007932, A045918. %K A334055 sign %O A334055 1,4 %A A334055 _Scott R. Shannon_, Sep 07 2020