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Primes p such that p + nextprime(p) is divisible by 5.
2

%I #16 Sep 08 2022 08:46:11

%S 2,13,29,43,47,59,103,113,149,157,163,167,179,193,199,223,239,257,269,

%T 293,313,367,401,419,463,491,509,557,569,587,599,607,613,619,643,647,

%U 659,673,677,701,727,761,773,809,823,853,863,883,911,947,953,977,1019

%N Primes p such that p + nextprime(p) is divisible by 5.

%C Primes p such that p + nextprime(p) is divisible by 10 is the same as this sequence without the term 2. - _Derek Orr_, Jan 30 2015

%H Harvey P. Dale, <a href="/A253970/b253970.txt">Table of n, a(n) for n = 1..1000</a>

%e p=29 is in this sequence because 29+31 = 60 is divisible by 5.

%t Prime@Select[Range[300], Mod[Prime[#] + Prime[# + 1], 5]==0 &]

%t Transpose[Select[Partition[Prime[Range[200]],2,1],Divisible[Total[ #],5]&]] [[1]] (* _Harvey P. Dale_, Feb 10 2015 *)

%o (Magma) [p: p in PrimesUpTo(1500) | (p+NextPrime(p)) mod 5 eq 0];

%o (PARI) forprime(p=1,10^3,if(!((p+nextprime(p+1))%5),print1(p,", "))) \\ _Derek Orr_, Jan 30 2015

%Y Cf. similar sequences listed in A253969.

%K nonn,easy

%O 1,1

%A _Vincenzo Librandi_, Jan 23 2015