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

1,2

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

Formula

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

Mathematica

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

Prog

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

Crossrefs

Cf. A001223.

Sequence in context: A248913 A227951 A102641 * A100374 A045841 A040003

Adjacent sequences: A054760 A054761 A054762 * A054764 A054765 A054766

Keyword

nonn

Author

Labos Elemer, May 17 2000

Status

approved