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 A187182 #17 Jan 31 2020 16:06:15
%S A187182 1,1,1,1,2,2,3,2,2,3,3,3,4,5,4,5,4,5,4,5,6,6,7,6,6,7,7,7,8,9,8,9,8,9,
%T A187182 8,9,10,10,11,10,10,11,11,11,12,13,12,13,12,13,12,13,14,14,15,14,14,
%U A187182 15,15,15,16,17,16,17,16,17,16,17,18,18,19,18,18,19,19,19,20,21,20,21,20,21,20,21,22,22,23,22,22,23,23,23,24,25,24,25,24,25,24,25
%N A187182 Parse the infinite string 0123012301230123... into distinct phrases 0, 1, 2, 3, 01, 23, 012, ...; a(n) = length of n-th phrase.
%C A187182 See A187180 for details.
%H A187182 Ray Chandler, <a href="/A187182/b187182.txt">Table of n, a(n) for n = 1..1000</a>
%H A187182 <a href="/index/Rec#order_17">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, 1, -1).
%F A187182 From _Colin Barker_, Jan 31 2020: (Start)
%F A187182 G.f.: x*(1 + x^4 + x^6 - x^7 + x^9 + x^12 + x^13 - x^14 + x^15 - 2*x^16 + x^17 - x^18 + x^19) / ((1 - x)^2*(1 + x)*(1 + x^2)*(1 + x^4)*(1 + x^8)).
%F A187182 a(n) = a(n-1) + a(n-16) - a(n-17) for n>20.
%F A187182 (End)
%e A187182 The sequence is quasi-periodic with period 16, increasing by 4 after each block:
%e A187182 1 1 1 1
%e A187182 2 2 3 2 2 3 3 3 4 5 4 5 4 5 4 5
%e A187182 6 6 7 6 6 7 7 7 8 9 8 9 8 9 8 9
%e A187182 10 10 11 10 10 11 11 11 12 13 12 13 12 13 12 13
%e A187182 14 14 15 14 14 15 15 15 16 17 16 17 16 17 16 17
%e A187182 ...
%t A187182 Join[{1, 1, 1},LinearRecurrence[{1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1},{1, 2, 2, 3, 2, 2, 3, 3, 3, 4, 5, 4, 5, 4, 5, 4, 5},97]] (* _Ray Chandler_, Aug 26 2015 *)
%o A187182 (PARI) Vec(x*(1 + x^4 + x^6 - x^7 + x^9 + x^12 + x^13 - x^14 + x^15 - 2*x^16 + x^17 - x^18 + x^19) / ((1 - x)^2*(1 + x)*(1 + x^2)*(1 + x^4)*(1 + x^8)) + O(x^80)) \\ _Colin Barker_, Jan 31 2020
%Y A187182 See A187180-A187188 for alphabets of size 2 through 10.
%K A187182 nonn,easy
%O A187182 1,5
%A A187182 _N. J. A. Sloane_, Mar 06 2011