A358002 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.

135, 936, 1431, 3510, 5005, 5106, 5278, 9471, 10648, 10659, 22126, 26724, 27420, 27840, 37014, 37149, 39321, 40311, 54730, 59031, 62830, 87186, 124914, 128616, 129411, 133494, 187705, 196078, 208285, 209451, 212695, 309885, 322191, 325465, 375513, 410515, 412476, 433041, 459844, 466620, 595833, 622083

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

Cf. A001414, A050703, A050704, A075254.

Sequence in context: A212610 A336554 A238330 * A157734 A334128 A210102

Adjacent sequences: A357999 A358000 A358001 * A358003 A358004 A358005

Keyword

nonn

Author

J. M. Bergot and Robert Israel, Oct 23 2022

Status

approved