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

Author

Antti Karttunen, Mar 16 2016

Keywords

• nonn

Links

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

Crossrefs

Complement: A269399.

Left inverse: A269362.

Cf. A270189.

Cf. also A270199.

Programs

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 *)

PARI

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

Formula

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

Other identities. For all n >= 1:

A269362(a(n)) = n.