OFFSET
1,1
COMMENTS
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.
LINKS
Robert Israel, Table of n, a(n) for n = 1..900
EXAMPLE
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.
MAPLE
filter:= proc(n) local t, s, x, y;
s:= add(t[1]*t[2], t = ifactors(n)[2]);
x:= s+n; y:= n-s;
if issqr(x) then isprime(sqrt(x)) and isprime(y)
else issqr(y) and isprime(sqrt(y)) and isprime(x)
fi
end proc:
select(filter, [$1..10^6]);
CROSSREFS
KEYWORD
nonn
AUTHOR
J. M. Bergot and Robert Israel, Oct 23 2022
STATUS
approved