A343454 Numbers k such that k^2+2*A001414(k) and k^2-2*A001414(k) are primes.

21, 33, 35, 39, 111, 339, 473, 629, 735, 779, 795, 801, 959, 1025, 1119, 1149, 1245, 1253, 1281, 1575, 1589, 1695, 1851, 1919, 1961, 1985, 2199, 2315, 2523, 2561, 2681, 2759, 3003, 3065, 3189, 3233, 3315, 3443, 3893, 3983, 4175, 4299, 4359, 4375, 4455, 4503, 4693, 4925, 5247, 5585, 5609, 5703

Offset: 1

Author

J. M. Bergot and Robert Israel, Apr 15 2021

Keywords

• nonn

Comments

Square roots of squares in A050705.

All terms are odd.

Includes 3*p if p, 9*p^2+2*p+6 and 9*p^2-2*p-6 are all primes; the generalized Bunyakovsky conjecture implies there are infinitely many of these.

Examples

			a(3) = 35 is a term because A001414(35) = 12 and 35^2-2*12 = 1201 and 35^2+2*12 = 1249 are primes.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001414, A050705.

Programs

Maple

spf:= n -> add(t[1]*t[2],t=ifactors(n)[2]):
filter:= proc(n) local s; s:= spf(n); isprime(n^2-2*s) and isprime(n^2+2*s) end proc:
select(filter, [seq(i,i=1..10000,2)]);