A269399 Numbers n for which prime(n+7)-prime(n+6) is a multiple of three.

3, 5, 9, 10, 12, 15, 17, 26, 30, 31, 33, 34, 40, 41, 45, 48, 49, 50, 52, 61, 65, 67, 68, 70, 78, 80, 85, 90, 91, 93, 94, 96, 97, 99, 101, 102, 104, 105, 108, 112, 113, 115, 117, 123, 124, 127, 133, 154, 155, 158, 159, 161, 162, 164, 168, 173, 174, 178, 179, 181, 182, 188, 189, 191, 193, 194, 196, 197, 199, 202, 204, 208, 210

Offset: 1

Author

Antti Karttunen, Mar 16 2016

Keywords

• nonn

Examples

			3 is present as the difference between A000040(3+7) = 29 and A000040(3+6) = 23 is 6, a multiple of three.
		

Links

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

Crossrefs

Complement: A269389.

Cf. A137264, A270190.

Cf. also A270199.

Programs

Mathematica

Select[Range@ 210, Divisible[Prime[# + 7] - Prime[# + 6], 3] &] (* Michael De Vlieger, Mar 18 2016 *)

PARI

isok(n) = ((prime(n+7) - prime(n+6)) % 3) == 0; \\ Michel Marcus, Mar 18 2016

Formula

a(n) = A270190(n) - 6.