

A253969


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


5



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
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OFFSET

1,1


COMMENTS

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


LINKS



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).


KEYWORD

nonn,easy


AUTHOR



STATUS

approved



