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%I #30 Sep 08 2022 08:46:11
%S 5,7,11,13,17,19,29,37,41,43,59,67,71,79,89,97,101,103,107,109,113,
%T 127,137,139,149,163,179,181,191,193,197,223,227,229,239,241,269,277,
%U 281,283,293,307,311,313,317,337,347,349,359,379,389,397,401,409,419,421
%N Primes p such that p + nextprime(p) is divisible by 6.
%C Sequence provides all primes p such that p + nextprime(p) is divisible by 3 (see Crossrefs).
%H Harvey P. Dale, <a href="/A253969/b253969.txt">Table of n, a(n) for n = 1..10000</a>
%e p=19 is in this sequence because 19+23 = 42 is divisible by 6.
%t Prime@Select[Range[200], Mod[Prime[#] + Prime[# + 1], 6]==0 &]
%t Select[Partition[Prime[Range[100]],2,1],Divisible[Total[#],6]&][[All,1]] (* _Harvey P. Dale_, Jan 20 2018 *)
%o (Magma) [p: p in PrimesUpTo(500) | (p+NextPrime(p)) mod 6 eq 0];
%o (PARI) forprime(p=1,10^3,if(!((p+nextprime(p+1))%6),print1(p,", "))) \\ _Derek Orr_, Jan 30 2015
%Y 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).
%K nonn,easy
%O 1,1
%A _Vincenzo Librandi_, Jan 21 2015
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