%I #7 Aug 26 2022 11:22:31
%S 11,13,17,29,31,37,43,47,61,67,71,73,79,83,101,103,107,113,127,131,
%T 139,149,163,179,191,193,199,211,227,233,241,269,277,281,311,317,331,
%U 353,373,389,409,419,443,457,523,563,569,577,599,613,643,647,659,683,691,701,719,739,743,769,773,787
%N Primes p such that the sum of p and the next four primes congruent mod 10 to p is 5 times a prime.
%H Robert Israel, <a href="/A356383/b356383.txt">Table of n, a(n) for n = 1..10000</a>
%e a(3) = 17 is a term because 17 is a prime, the next four primes == 17 (mod 10) are 37, 47, 67 and 97 and 17+37+47+67+97 = 265 = 5*53 where 53 is prime.
%p filter:= proc(p) local q,s,k;
%p if not isprime(p) then return false fi;
%p s:= p; k:= 1;
%p for q from p+10 by 10 while k < 5 do
%p if isprime(q) then k:= k+1; s:= s+q; fi
%p od;
%p isprime(s/5)
%p end proc:
%p filter(5):= false:
%p select(filter, [seq(i,i=3..1000,2)]);
%K nonn
%O 1,1
%A _J. M. Bergot_ and _Robert Israel_, Aug 05 2022