A338476 Primes of the form 398*x^2-1.

397, 3581, 6367, 9949, 14327, 19501, 25471, 32237, 39799, 48157, 67261, 78007, 115021, 128951, 143677, 159199, 192631, 229247, 248749, 290141, 312031, 334717, 433421, 460087, 544861, 574711, 735901, 770527, 842167, 879181, 1035197, 1076191, 1160567, 1203949, 1338871, 1385437, 1432799, 1786621

Offset

1,1

Comments

There are 414 such primes for 1 <= x <= 1000, and 3280 for 1 <= x <= 10000.

Links

Table of n, a(n) for n=1..38.

V. Granville, Quadratic progressions with very high prime density, MathOverflow.

Formula

a(n) = 398*A338477(n)^2-1.

Example

a(3) = 398*4^2-1 = 6367 is prime.

Maple

select(isprime, [seq(398*x^2-1, x=1..1000)]);

Mathematica

Select[398 Range[100]^2-1, PrimeQ] (* Harvey P. Dale, Jan 13 2023 *)

Crossrefs

Cf. A331947(11)=398, A338477.

Sequence in context: A038660 A129190 A256081 * A152309 A298124 A327592

Adjacent sequences: A338473 A338474 A338475 * A338477 A338478 A338479

Keyword

nonn

Author

Robert Israel, Oct 29 2020

Status

approved