A270189 Numbers n for which (prime(n+1)-prime(n)) is not a multiple of three.

1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 13, 14, 17, 19, 20, 22, 24, 25, 26, 27, 28, 29, 30, 31, 33, 34, 35, 38, 41, 42, 43, 44, 45, 48, 49, 50, 52, 53, 57, 59, 60, 61, 62, 63, 64, 65, 66, 68, 69, 70, 72, 75, 77, 78, 79, 80, 81, 82, 83, 85, 87, 88, 89, 90, 92, 93, 94, 95, 98, 101, 104, 106, 109, 112, 113, 115, 116, 117, 120, 122, 124, 125

Offset: 1

Author

Antti Karttunen, Mar 16 2016

Keywords

• nonn

Comments

See A269364 for the effect of the bias that favors these terms over the terms of A270190.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000
• Terence Tao, Biases between consecutive primes, blog entry March 14, 2016

Crossrefs

Complement: A270190.

Disjoint union of A270191 and A270192.

Positions of 1's and 2's in A137264.

Left inverse: A269849.

Cf. A000040, A001223, A269364, A269389.

Programs

Mathematica

Select[Range@ 125, Mod[Prime[# + 1] - Prime@ #, 3] != 0 &] (* Michael De Vlieger, Mar 17 2016 *)

PARI

isok(n) = ((prime(n+1) - prime(n)) % 3) != 0; \\ Michel Marcus, Mar 17 2016

Formula

Other identities. For all n >= 1:

A269849(a(n)) = n.