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%I #28 Mar 12 2021 19:33:48
%S 11,13,19,23,31,41,53,59,61,67,79,89,103,139,167,179,193,199,241,251,
%T 257,277,347,367,373,409,461,463,467,479,523,541,563,601,613,641,653,
%U 691,719,743,811,823,853,881,887,937,947,977,1039,1063,1087,1117,1129,1151,1223,1249,1259,1277,1283
%N Primes p such that the number of ways to write p = 2*q + r with q and r prime is a prime.
%C Primes prime(k) such that A103274(k) is prime.
%H Robert Israel, <a href="/A342406/b342406.txt">Table of n, a(n) for n = 1..1000</a>
%e a(3) = 19 because there are 2 ways: 19 = 2*3+13 = 2*7+5, and 2 is prime.
%p filter:= proc(p) local q, count;
%p q:= 1; count:= 0;
%p do
%p q:= nextprime(q);
%p if 2*q >= p then return isprime(count) fi;
%p if isprime(p-2*q) then count:= count+1 fi
%p od
%p end proc:
%p select(filter, [seq(ithprime(i),i=1..1000)]);
%Y Cf. A103274.
%K nonn
%O 1,1
%A _J. M. Bergot_ and _Robert Israel_, Mar 11 2021
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