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

1,1

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.

Links

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

Example

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

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)]);

Crossrefs

Cf. A001414, A050705.

Sequence in context: A219881 A181677 A036382 * A368949 A298855 A354813

Adjacent sequences: A343451 A343452 A343453 * A343455 A343456 A343457

Keyword

nonn

Author

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

Status

approved