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

1,2

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

Formula

Other identities. For all n >= 1:

A269849(a(n)) = n.

Mathematica

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

Prog

(Scheme, with Antti Karttunen's IntSeq-library)
(define A270189 (NONZERO-POS 1 1 A137264))
(PARI) isok(n) = ((prime(n+1) - prime(n)) % 3) != 0; \\ Michel Marcus, Mar 17 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.

Sequence in context: A263977 A335040 A270427 * A257672 A285314 A080544

Adjacent sequences: A270186 A270187 A270188 * A270190 A270191 A270192

Keyword

nonn

Author

Antti Karttunen, Mar 16 2016

Status

approved