A253969 Primes p such that p + nextprime(p) is divisible by 6.

5, 7, 11, 13, 17, 19, 29, 37, 41, 43, 59, 67, 71, 79, 89, 97, 101, 103, 107, 109, 113, 127, 137, 139, 149, 163, 179, 181, 191, 193, 197, 223, 227, 229, 239, 241, 269, 277, 281, 283, 293, 307, 311, 313, 317, 337, 347, 349, 359, 379, 389, 397, 401, 409, 419, 421

Offset

1,1

Comments

Sequence provides all primes p such that p + nextprime(p) is divisible by 3 (see Crossrefs).

Links

Harvey P. Dale, Table of n, a(n) for n = 1..10000

Example

p=19 is in this sequence because 19+23 = 42 is divisible by 6.

Mathematica

Prime@Select[Range[200], Mod[Prime[#] + Prime[# + 1], 6]==0 &]
Select[Partition[Prime[Range[100]], 2, 1], Divisible[Total[#], 6]&][[All, 1]] (* Harvey P. Dale, Jan 20 2018 *)

Prog

(Magma) [p: p in PrimesUpTo(500) | (p+NextPrime(p)) mod 6 eq 0];
(PARI) forprime(p=1, 10^3, if(!((p+nextprime(p+1))%6), print1(p, ", "))) \\ Derek Orr, Jan 30 2015

Crossrefs

Cf. sum of prime p and next prime after p is divisible by k: A000040 (k=2, after the first term), this sequence (k=3, k=6), A098058(k=4, after the first term), A253970 (k=5; k=10 without 2), A179849 (k=7), A253972 (k=8), A253973 (k=9).

Sequence in context: A171688 A239711 A217090 * A191056 A314296 A141639

Adjacent sequences: A253966 A253967 A253968 * A253970 A253971 A253972

Keyword

nonn,easy

Author

Vincenzo Librandi, Jan 21 2015

Status

approved