A359184 Numbers k such that 30*k - 1, 30*k + 1, 30*k^2 - 1 and 30*k^2 + 1 are all prime.

1, 14, 118, 232, 538, 720, 1155, 1253, 2821, 3151, 6161, 6238, 6916, 7428, 7827, 9009, 9521, 9933, 10284, 10779, 11661, 12348, 13663, 13811, 14092, 14938, 15273, 16323, 16457, 17116, 17940, 20735, 21931, 22022, 24010, 24311, 24375, 26557, 28293, 29645, 30555, 33880, 34033, 34328, 35797, 36413

Offset

1,2

Comments

Numbers k such that 30*k and 30*k^2 are in A014574.

The first number k > 1 such that 30*k - 1, 30*k + 1, 30*k^2 - 1, 30*k^2 + 1, 30*k^3 - 1 and 30*k^3 + 1 are all prime is 266225.

Links

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

Example

a(2) = 14 is a term because 30*14 - 1 = 419, 30*14 + 1 = 421, 30*14^2 - 1 = 5879, and 30*14^2 + 1 = 5881 are all prime.

Maple

select(k -> isprime(30*k-1) and isprime(30*k+1) and isprime(30*k^2-1) and isprime(30*k^2+1), [$1..10^5]);

Mathematica

Select[Range[40000], AllTrue[{30*# - 1, 30*# + 1, 30*#^2 - 1, 30*#^2 + 1}, PrimeQ] &] (* Amiram Eldar, Dec 19 2022 *)

Crossrefs

Cf. A014574.

Intersection of A176114 and A283867.

Sequence in context: A128569 A138431 A175874 * A006223 A091303 A241463

Adjacent sequences: A359181 A359182 A359183 * A359185 A359186 A359187

Keyword

nonn

Author

Robert Israel, Dec 18 2022

Status

approved