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 A187188 #18 Aug 26 2015 16:58:36 %S A187188 1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,3,2,2,2,2,2,3,3,3,3,3,3,3,3,3,4,4,4,4, %T A187188 4,5,4,4,4,4,4,5,6,5,5,6,5,5,6,5,5,6,5,5,6,7,6,6,6,6,6,7,7,7,7,7,7,7, %U A187188 7,7,8,8,8,8,8,9,8,8,8,8,8,9,9,9,9,9,9,9,9,9,10,11,10,11,10,11,10,11,10,11,10,11,10,11,10,11,10,11,10,11,12,12,12,12,12,13,12,12,12,12 %N A187188 Parse the infinite string 0123456789012345678901234567890... into distinct phrases 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 01, 23, 45, 67, 89, 012, 34, 56, 78, 90, 12, 345, ...; a(n) = length of n-th phrase. %C A187188 See A187180-A187187 for further details. %C A187188 Answers a question raised by Sergio Verdu (personal communication, Mar 05 2011). %H A187188 N. J. A. Sloane, <a href="/A187188/b187188.txt">Table of n, a(n) for n = 1..1000</a> %H A187188 <a href="/index/Rec#order_101">Index entries for linear recurrences with constant coefficients</a>, signature (1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1). %F A187188 After the initial block of 10 1's, the sequence is quasi-periodic with period 100, increasing by 10 after each block. In more detail: %F A187188 a(n) = 1 for 1 <= n <= 10. %F A187188 For n >= 10, write n = 11 + 100i + j with i >= 0, 0 <= j <= 99. %F A187188 Then for 0 <= j <= 79, a(n) = 10i + f(j), %F A187188 where f(0) ... f(79) is the following 80-term sequence: %F A187188 [2 2 2 2 2 3 2 2 2 2 2 3 %F A187188 3 3 3 3 3 3 3 3 %F A187188 4 4 4 4 4 5 4 4 4 4 4 5 %F A187188 6 5 5 6 5 5 6 5 5 6 5 5 %F A187188 6 7 %F A187188 6 6 6 6 6 %F A187188 7 7 7 7 7 7 7 7 7 %F A187188 8 8 8 8 8 9 8 8 8 8 8 9 %F A187188 9 9 9 9 9 9 9 9] %F A187188 (this has been broken into blocks to make it easier to see), %F A187188 and for 80 <= j <= 99, a(n) = 10i+10 if j is even, a(n) = 10i+11 if j is odd. %F A187188 Examples: %F A187188 n=120 = 11 + 100*1 + 9, i=1, j=9, a(120)=10+f(9) = 10+2 = 12 %F A187188 n=292 = 11 + 100*2 + 81, i=2, j=81. a(292)=20+11=31 %e A187188 The sequence begins %e A187188 1 1 1 1 1 1 1 1 1 1 %e A187188 2 2 2 2 2 3 2 2 2 2 2 3 %e A187188 3 3 3 3 3 3 3 3 %e A187188 4 4 4 4 4 5 4 4 4 4 4 5 %e A187188 6 5 5 6 5 5 6 5 5 6 5 5 %e A187188 6 7 %e A187188 6 6 6 6 6 %e A187188 7 7 7 7 7 7 7 7 7 %e A187188 8 8 8 8 8 9 8 8 8 8 8 9 %e A187188 9 9 9 9 9 9 9 9 %e A187188 10 11 10 11 10 11 10 11 10 11 10 11 10 11 10 11 10 11 10 11 %e A187188 12 12 12 12 12 13 12 12 12 12 12 13 %e A187188 ... %Y A187188 See A187180-A187188 for alphabets of size 2 through 10. %Y A187188 See also A109337, A187199, A187200. %K A187188 nonn %O A187188 1,11 %A A187188 _N. J. A. Sloane_, Mar 06 2011