A359184 - OEIS

%I #15 Dec 22 2022 02:10:33

%S 1,14,118,232,538,720,1155,1253,2821,3151,6161,6238,6916,7428,7827,

%T 9009,9521,9933,10284,10779,11661,12348,13663,13811,14092,14938,15273,

%U 16323,16457,17116,17940,20735,21931,22022,24010,24311,24375,26557,28293,29645,30555,33880,34033,34328,35797,36413

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

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

%C 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.

%H Robert Israel, <a href="/A359184/b359184.txt">Table of n, a(n) for n = 1..10000</a>

%e 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.

%p 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]);

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

%Y Cf. A014574.

%Y Intersection of A176114 and A283867.

%K nonn

%O 1,2

%A _Robert Israel_, Dec 18 2022