

A054763


Residues of consecutive prime differences modulo 6.


5



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
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OFFSET

1,2


COMMENTS

For n>2, only the 0residues 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)=6nz(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



