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 A245979 #11 Jun 14 2025 21:50:40
%S A245979 5,3,5,5,8,8,5,8,13,8,13,8,13,13,8,13,13,21,21,13,21,21,13,21,13,21,
%T A245979 21,13,21,34,21,34,21,34,34,21,34,21,34,34,21,34,34,21,34,21,34,34,21,
%U A245979 34,34,55,55,34,55,55,34,55,34,55,55,34,55,55,34,55,34
%N A245979 First differences of A245978.
%C A245979 It appears that every term is a Fibonacci number, as in A000045. The sequence A245979 arises from A245977 and A245978 in the following manner.
%C A245979 Suppose, as in A245920, that S = (s(0),s(1),s(2),...) is an infinite sequence such that every finite block of consecutive terms occurs infinitely many times in S. (It is assumed that A014675 is such a sequence.) Let B = B(m,k) = (s(m-k),s(m-k+1),...,s(m)) be such a block, where m >= 0 and k >= 0. Let m(1) be the least i > m such that (s(i-k),s(i-k+1),...,s(i)) = B(m,k), and put B(m(1),k+1) = (s(m(1)-k-1),s(m(1)-k),...,s(m(1))). Let m(2) be the least i > m(1) such that (s(i-k-1),s(i-k),...,s(i)) = B(m(1),k+1), and put B(m(2),k+2) = (s(m(2)-k-2),s(m(2)-k-1),...,s(m(2))). Continuing in this manner gives a sequence of blocks B(m(n),k+n). Let B'(n) = reverse(B(m(n),k+n)), so that for n >= 1, B'(n) comes from B'(n-1) by suffixing a single term; thus the limit of B'(n) is defined; we call it the "limit-reverse of S with initial block B(m,k)", denoted by S*(m,k), or simply S*.
%C A245979 ...
%C A245979 The sequence (m(i)), where m(0) = 0, is the "index sequence for limit-reversing S with initial block B(m,k)" or simply the index sequence for S*, as in A245921 and A245978. Then A245979 is the difference sequence of A245978, as in the Example.
%e A245979 S = the infinite Fibonacci word A014675, with B = (s(2),s(3)); that is, (m,k) = (2,3)
%e A245979 S = (2,1,2,2,1,2,1,2,2,1,2,2,1,2,1,2,2,1,2,...)
%e A245979 B'(0) = (2,2)
%e A245979 B'(1) = (2,2,1)
%e A245979 B'(2) = (2,2,1,2)
%e A245979 B'(3) = (2,2,1,2,1)
%e A245979 B'(4) = (2,2,1,2,1,2)
%e A245979 B'(5) = (2,2,1,2,1,2,2)
%e A245979 S* = (2,2,1,2,1,2,2,1,2,2,1,2,1,2,2,1,2,1,...), with index sequence (3,8,11,16,21,29,...), of which the difference sequence is (5,3,5,5,8,8,5,8,13,8,...)
%t A245979 z = 140; seqPosition2[list_, seqtofind_] := Last[Last[Position[Partition[list, Length[#], 1], Flatten[{___, #, ___}], 1, 2]]] &[seqtofind]; x = GoldenRatio; s = Differences[Table[Floor[n*x], {n, 1, z^2}]]; ans = Join[{s[[p[0] = pos = seqPosition2[s, #] - 1]]}, #] &[{s[[3]], s[[4]]}]; (* Initial block is (s(3),s(4)) [OR (s(2),s(3)) if using offset 0] *)
%t A245979 cfs = Table[s = Drop[s, pos - 1]; ans = Join[{s[[p[n] = pos = seqPosition2[s, #] - 1]]}, #] &[ans], {n, z}]; q = Join[{3}, Rest[Accumulate[Join[{1}, Table[p[n], {n, 0, z}]]]]] (* A245978 *)
%t A245979 q1 = Differences[q] (* A245979 *)
%Y A245979 Cf. A245978, A245977, A245979, A245921, A014675, A000045.
%K A245979 nonn
%O A245979 1,1
%A A245979 _Clark Kimberling_ and _Peter J. C. Moses_, Aug 10 2014