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 A054763 #24 Mar 06 2017 03:48:49 %S A054763 1,2,2,4,2,4,2,4,0,2,0,4,2,4,0,0,2,0,4,2,0,4,0,2,4,2,4,2,4,2,4,0,2,4, %T A054763 2,0,0,4,0,0,2,4,2,4,2,0,0,4,2,4,0,2,4,0,0,0,2,0,4,2,4,2,4,2,4,2,0,4, %U A054763 2,4,0,2,0,0,4,0,2,4,2,4,2,4,2,0,4,0,2,4,2,4,0,2,4,2,4,0,0,2,0,0,4,0,0,2,0 %N A054763 Residues of consecutive prime differences modulo 6. %C A054763 For n>2, only the 0-residues may arise several times after each other, that is, there are no "2,2" and no "4,4". Let nz(k) denote the nonzero values of A054763(n). Then nz(0)=1, nz(1)=2, nz(2)=2, and nz(k+1)=6-nz(k) for k>1. Conjecture: the percentage of zeros in A054763(n) asymptotically runs to 50%. - _Alex Ratushnyak_, Apr 18 2012 %H A054763 Michael De Vlieger, <a href="/A054763/b054763.txt">Table of n, a(n) for n = 1..10000</a> %F A054763 a(n) = A001223(n) mod 6. %t A054763 Mod[#, 6] & /@ Differences@ Prime@ Range@ 105 (* _Michael De Vlieger_, Mar 05 2017 *) %o A054763 (PARI) a(n) = (prime(n+1) - prime(n)) % 6; \\ _Michel Marcus_, Dec 17 2013 %Y A054763 Cf. A001223. %K A054763 nonn %O A054763 1,2 %A A054763 _Labos Elemer_, May 17 2000