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 A105470 #9 Oct 13 2019 10:13:55
%S A105470 1,1,0,1,0,1,0,1,1,0,1,1,0,1,1,1,0,1,1,0,1,1,1,1,1,0,1,0,1,1,1,1,0,1,
%T A105470 0,1,1,1,1,1,0,1,0,1,0,1,1,1,0,1,1,0,1,1,1,1,0,1,1,0,1,1,1,0,1,1,1,1,
%U A105470 0,1,1,1,1,1,1,1,1,1,1,1,0,1,0,1,1,1,1,1,0,1,1,1,1,1,1,1,1,0,1,1,1,1,1,0,1
%N A105470 a(n)=1 if there is number of the form 6k+3 with prime(n) <= 6k+3 <= prime(n+1), otherwise 0.
%C A105470 Except for the first pair of primes and for twin primes there is always at least one number of the form 6n+3 between two successive primes.
%e A105470 a(3)=0 because between prime(3) and prime(4) there are no numbers of the form 6k+3;
%e A105470 a(4)=1 because between prime(4) and prime(5) there is one number of the form 6k+3: 9.
%t A105470 f[n_] := Count[Table[Mod[k, 6], {k, Prime[n], Prime[n + 1]}], 3];Table[If[f[n] == 0, 0, 1], {n, 120}] (* _Ray Chandler_, Oct 17 2006 *)
%t A105470 Join[{1,1},If[Last[#]-First[#]==2,0,1]&/@Partition[Prime[Range[ 3,200]],2,1]] (* _Harvey P. Dale_, Nov 27 2013 *)
%Y A105470 Cf. A100810, A106002.
%K A105470 easy,nonn
%O A105470 1,1
%A A105470 _Giovanni Teofilatto_, May 02 2005
%E A105470 Edited by _Ray Chandler_, Oct 17 2006