A269389 Numbers n for which prime(n+7)-prime(n+6) is not a multiple of three.

1, 2, 4, 6, 7, 8, 11, 13, 14, 16, 18, 19, 20, 21, 22, 23, 24, 25, 27, 28, 29, 32, 35, 36, 37, 38, 39, 42, 43, 44, 46, 47, 51, 53, 54, 55, 56, 57, 58, 59, 60, 62, 63, 64, 66, 69, 71, 72, 73, 74, 75, 76, 77, 79, 81, 82, 83, 84, 86, 87, 88, 89, 92, 95, 98, 100, 103, 106, 107, 109, 110, 111, 114, 116, 118, 119, 120, 121, 122, 125

Offset

1,2

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000

Formula

a(n) = A270189(6+n) - 6.

Other identities. For all n >= 1:

A269362(a(n)) = n.

Mathematica

Select[Range@ 125, ! Divisible[Prime[# + 7] - Prime[# + 6], 3] &] (* Michael De Vlieger, Mar 18 2016 *)
Drop[Flatten[Position[Partition[Prime[Range[200]], 2, 1], _?(Mod[#[[2]]- #[[1]], 3]!=0&), 1, Heads->False]], 6]-6 (* Harvey P. Dale, Dec 17 2018 *)

Prog

(Scheme, with Antti Karttunen's IntSeq-library)
(define A269389 (MATCHING-POS 1 1 (lambda (n) (< 0 (A137264 (+ 6 n))))))
(PARI) isok(n) = ((prime(n+7) - prime(n+6)) % 3) != 0; \\ Michel Marcus, Mar 18 2016

Crossrefs

Complement: A269399.

Left inverse: A269362.

Cf. A270189.

Cf. also A270199.

Sequence in context: A139527 A163578 A345918 * A092054 A334573 A228370

Adjacent sequences: A269386 A269387 A269388 * A269390 A269391 A269392

Keyword

nonn

Author

Antti Karttunen, Mar 16 2016

Status

approved