A390794 Numbers of the form p^2 - b^2 where p is prime and b > 0.

3, 5, 8, 9, 13, 16, 21, 24, 25, 33, 37, 40, 45, 48, 57, 61, 64, 69, 72, 73, 81, 85, 88, 93, 96, 105, 112, 117, 120, 121, 129, 133, 136, 141, 144, 145, 153, 157, 160, 165, 168, 177, 184, 189, 192, 193, 201, 205, 208, 213, 216, 217, 225, 232, 237, 240, 249, 253, 261, 264, 265, 273, 277, 280, 285

Offset

1,1

Comments

Numbers k with at least one divisor d < sqrt(k) such that (d + k/d)/2 is prime.

Links

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

Example

a(5) = 13 is a term because 13 = 7^2 - 6^2 where 7 is prime.

Maple

filter:= proc(n) ormap(t -> (t+n/t)::even and t > n/t and isprime((t + n/t)/2), NumberTheory:-Divisors(n)) end proc:
select(filter, [$1..300]);

Crossrefs

Includes A005383.

Cf. A355643.

Sequence in context: A186621 A002159 A050094 * A137319 A384628 A138808

Adjacent sequences: A390791 A390792 A390793 * A390795 A390796 A390797

Keyword

nonn

Author

Will Gosnell and Robert Israel, Jan 31 2026

Status

approved