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 A300004 #12 Mar 19 2018 22:30:03
%S A300004 4,2,4,2,4,6,2,6,6,4,2,4,6,2,10,2,4,2,10,2,6,4,2,4,2,4,8,6,4,2,4,2,4,
%T A300004 6,8,4,2,6,4,6,2,6,4,2,6,4,8,6,4,6,2,4,6,2,6,6,4,2,4,6,2,6,4,2,4,2,10,
%U A300004 8,4,2,4,2,4,8,6,4,2,4,2,10,2,6,6,10,6,2,6,4,2,4,2,4,8,6,6,4,2,4,6,2,12,4,2,4
%N A300004 First differences of the list A292794 of numbers not congruent to F(k) modulo F(k+1) for any k > 1, where F are the Fibonacci numbers A000045.
%C A300004 The sequence has been chosen 0-indexed, as for A292794.
%C A300004 It has been conjectured that every even number occurs in this sequence.
%C A300004 It would be interesting to know whether there are patterns or formulae for the indices at which the respective even numbers occur.
%C A300004 The index of the first occurrence of 2n in this sequence is listed in A300004 = (1, 0, 5, 26, 14, ...): a(1), a(0), a(5), a(26), a(14), ... is the first occurrence of 2, 4, 6, 8, 10, ... in this sequence.
%F A300004 a(n) = A292794(n+1) - A292794(n).
%t A300004 Differences@ Join[{0}, Select[Range[3, 500], Function[n, NoneTrue[Block[{k = {1, 1}}, While[Last@k <= n, AppendTo[k, Total@ Take[k, -2]]]; Partition[Most@ k, 2, 1]], Mod[n, #2] == #1 & @@ # &]]]] (* _Michael De Vlieger_, Mar 19 2018 *)
%o A300004 (PARI) (D(v)=v[^1]-v[^-1])(A292794=select(is_A292794,[0..500]))
%o A300004 (PARI) print1(L=0); for(n=1,oo, is_A292794(n)&&print1(",",-L+L=n))
%Y A300004 Cf. A292794, A000045.
%K A300004 nonn
%O A300004 0,1
%A A300004 _M. F. Hasler_, Feb 25 2018
%E A300004 Edited by _M. F. Hasler_, Mar 05 2018