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A187183 Parse the infinite string 012340123401234012340... into distinct phrases 0, 1, 2, 3, 4, 01, 23, 40, 12, ...; a(n) = length of n-th phrase.

%I A187183 #15 Jan 31 2020 16:06:22
%S A187183 1,1,1,1,1,2,2,2,2,2,3,3,3,3,3,4,4,4,4,4,5,6,5,6,5,6,5,6,5,6,7,7,7,7,
%T A187183 7,8,8,8,8,8,9,9,9,9,9,10,11,10,11,10,11,10,11,10,11,12,12,12,12,12,
%U A187183 13,13,13,13,13,14,14,14,14,14,15,16,15,16,15,16,15,16,15,16,17,17,17,17,17,18,18,18,18,18,19,19,19,19,19,20,21,20,21,20
%N A187183 Parse the infinite string 012340123401234012340... into distinct phrases 0, 1, 2, 3, 4, 01, 23, 40, 12, ...; a(n) = length of n-th phrase.
%C A187183 See A187180 for details.
%H A187183 Ray Chandler, <a href="/A187183/b187183.txt">Table of n, a(n) for n = 1..1000</a>
%H A187183 <a href="/index/Rec#order_26">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, 1, -1).
%F A187183 After the initial block of five 1's, the sequence is quasi-periodic with period 25, increasing by 5 after each block.
%F A187183 From _Colin Barker_, Jan 31 2020: (Start)
%F A187183 G.f.: x*(1 + x^5 + x^10 + x^15 + x^20 + x^21 - x^22 + x^23 - x^24 - x^26 + x^27 - x^28 + x^29) / ((1 - x)^2*(1 + x + x^2 + x^3 + x^4)*(1 + x^5 + x^10 + x^15 + x^20)).
%F A187183 a(n) = a(n-1) + a(n-25) - a(n-26) for n>30.
%F A187183 (End)
%t A187183 Join[{1, 1, 1, 1},LinearRecurrence[{1, 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},{1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 6, 5, 6, 5, 6, 5, 6, 5, 6},96]] (* _Ray Chandler_, Aug 26 2015 *)
%o A187183 (PARI) Vec(x*(1 + x^5 + x^10 + x^15 + x^20 + x^21 - x^22 + x^23 - x^24 - x^26 + x^27 - x^28 + x^29) / ((1 - x)^2*(1 + x + x^2 + x^3 + x^4)*(1 + x^5 + x^10 + x^15 + x^20)) + O(x^80)) \\ _Colin Barker_, Jan 31 2020
%Y A187183 See A187180-A187188 for alphabets of size 2 through 10.
%K A187183 nonn,easy
%O A187183 1,6
%A A187183 _N. J. A. Sloane_, Mar 06 2011