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%I #17 Oct 25 2022 20:04:57
%S 135,936,1431,3510,5005,5106,5278,9471,10648,10659,22126,26724,27420,
%T 27840,37014,37149,39321,40311,54730,59031,62830,87186,124914,128616,
%U 129411,133494,187705,196078,208285,209451,212695,309885,322191,325465,375513,410515,412476,433041,459844,466620,595833,622083
%N Numbers k such that one of k-A001414(k) and k+A001414(k) is a prime and the other is the square of a prime.
%C The Generalized Bunyakovsky conjecture implies that there are, for example, infinitely many primes q == 11 (mod 26) such that p = (q^2+9)/26 and 28*p+9 are prime, and then 27*p is in the sequence.
%H Robert Israel, <a href="/A358002/b358002.txt">Table of n, a(n) for n = 1..900</a>
%e a(4) = 3510 is a term because 3510 = 2*3^3*5*13 so A001414(3510) = 2+3*3+5+13 = 29 and 3510-29 = 3481 = 29^2 is the square of a prime, while 3510+29 = 3539 is prime.
%p filter:= proc(n) local t,s,x,y;
%p s:= add(t[1]*t[2], t = ifactors(n)[2]);
%p x:= s+n; y:= n-s;
%p if issqr(x) then isprime(sqrt(x)) and isprime(y)
%p else issqr(y) and isprime(sqrt(y)) and isprime(x)
%p fi
%p end proc:
%p select(filter, [$1..10^6]);
%Y Cf. A001414, A050703, A050704, A075254.
%K nonn
%O 1,1
%A _J. M. Bergot_ and _Robert Israel_, Oct 23 2022
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