A179849 -id:A179849 - cp's OEIS frontend

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

Vincenzo Librandi, Jan 21 2015

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

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

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

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).

[p: p in PrimesUpTo(500) | (p+NextPrime(p)) mod 6 eq 0];

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 *)

forprime(p=1,10^3,if(!((p+nextprime(p+1))%6),print1(p,", "))) \\ Derek Orr, Jan 30 2015

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

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