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Primes p such that if q is the next prime, (p+q)/5+5 is prime.
1

%I #23 Mar 23 2022 12:49:22

%S 13,29,43,59,103,113,163,167,193,239,257,269,313,401,419,463,509,557,

%T 569,587,613,643,659,677,761,773,853,863,883,953,977,1093,1129,1213,

%U 1289,1483,1499,1583,1619,1693,1709,1783,1907,2083,2129,2203,2309,2339,2399,2423,2531,2579,2633,2729,2741

%N Primes p such that if q is the next prime, (p+q)/5+5 is prime.

%H Robert Israel, <a href="/A351387/b351387.txt">Table of n, a(n) for n = 1..10000</a>

%e a(3) = 43 is a term because 47 is the next prime and (43+47)/5+5 = 23 is prime.

%p N:= 3000: # for terms <= N

%p Primes:= select(isprime,[2,seq(i,i=3..nextprime(N),2)]):

%p nP:= nops(Primes):

%p L:=(Primes[1..nP-1]+Primes[2..nP])/5 +~ 5:

%p Primes[select(i -> L[i]::integer and isprime(L[i]), [$1..nP-1])];

%K nonn

%O 1,1

%A _J. M. Bergot_ and _Robert Israel_, Mar 20 2022