A338477 Numbers k such that 398*k^2 - 1 is prime.

1, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 17, 18, 19, 20, 22, 24, 25, 27, 28, 29, 33, 34, 37, 38, 43, 44, 46, 47, 51, 52, 54, 55, 58, 59, 60, 67, 68, 71, 73, 75, 79, 80, 81, 82, 83, 85, 86, 87, 89, 90, 93, 94, 95, 96, 97, 100, 103, 106, 107, 108, 110, 112, 114, 116, 117, 119, 121, 124, 125, 128

Offset

1,2

Comments

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

Links

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

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

Formula

a(n) = sqrt(A338476(n) + 1)/398.

Example

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

Maple

select(t -> isprime(398*t^2-1), [$1..1000]);

Crossrefs

Cf. A338476.

Cf. A331947, where 398 is a term.

Sequence in context: A026417 A026421 A026481 * A039211 A114035 A329779

Adjacent sequences: A338474 A338475 A338476 * A338478 A338479 A338480

Keyword

nonn

Author

Robert Israel, Oct 29 2020

Status

approved