A392481 Numbers k such that both (3*k-3)^2 + k^2 and (3*k)^2 + (k+1)^2 are prime.

10, 16, 85, 169, 211, 229, 289, 349, 361, 445, 451, 484, 544, 700, 826, 835, 844, 955, 1066, 1111, 1156, 1231, 1351, 1420, 1480, 1501, 1576, 1855, 1945, 2044, 2050, 2086, 2116, 2161, 2200, 2335, 2350, 2494, 2620, 2659, 2815, 3214, 3250, 3271, 3334, 3400, 3406, 3454, 3520, 3571, 3664, 3715, 3769, 3871

Offset

1,1

Comments

All terms == 1 (mod 3).

Links

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

Example

a(3) = 85 is a term because (3*85-3)^2 + 85^2 = 70729 and (3*85)^2 + 86^2 = 72421 are both primes.

Maple

filter:= t -> isprime((3*t-3)^2 + t^2) and isprime((3*t)^2 + (t+1)^2):
select(filter, [$1..10000]);

Mathematica

Select[Range[1, 5000, 3], PrimeQ[2*#*(5*#-9) + 9] && PrimeQ[2*#*(5*#+1) + 1] &] (* Paolo Xausa, Jan 15 2026 *)

Crossrefs

Sequence in context: A033460 A056848 A219854 * A167331 A255531 A157159

Adjacent sequences: A392478 A392479 A392480 * A392482 A392483 A392484

Keyword

nonn

Author

Will Gosnell and Robert Israel, Jan 13 2026

Status

approved