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

Author

Robert Israel, Dec 18 2022

Keywords

• nonn

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.

Examples

			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.
		

Links

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

Crossrefs

Cf. A014574.

Intersection of A176114 and A283867.

Programs

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 *)