A054763 Residues of consecutive prime differences modulo 6.

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, 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, 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

Offset: 1

Author

Labos Elemer, May 17 2000

Keywords

• nonn

Comments

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

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001223.

Programs

Mathematica

Mod[#, 6] & /@ Differences@ Prime@ Range@ 105 (* Michael De Vlieger, Mar 05 2017 *)

PARI

a(n) = (prime(n+1) - prime(n)) % 6; \\ Michel Marcus, Dec 17 2013

Formula

a(n) = A001223(n) mod 6.