A253940 - OEIS

%I #13 Sep 08 2022 08:46:11

%S 39367,52163,67103,79631,100981,280547,318457,530711,605123,815401,

%T 833923,834947,928871,1313857,1734067,1750069,1800973,2163979,2427137,

%U 2598119,2611027,2754991,2764187,2836259,3040757,3101309,3118697,3465953,3646693,4014809

%N Primes p such that (p^2 + 5)/6, (p^4 + 5)/6, and (p^8 + 5)/6 are prime.

%H R. J. Mathar, <a href="/A253940/b253940.txt">Table of n, a(n) for n = 1..108</a>

%t Select[Prime[Range[10^6]], PrimeQ[(#^2 + 5) / 6] &&PrimeQ[(#^4 + 5) / 6] &&PrimeQ[(#^8 + 5) / 6] &] (* _Vincenzo Librandi_, Jan 21 2015 *)

%t Select[Prime[Range[300000]],AllTrue[({#^2,#^4,#^8}+5)/6,PrimeQ]&] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Jul 15 2021 *)

%o (Magma) [p: p in PrimesUpTo(10^7) | IsPrime((p^2+5) div 6) and IsPrime((p^4+5) div 6) and IsPrime((p^8+5) div 6)]; // _Vincenzo Librandi_, Jan 21 2015

%Y Subsequence of A253925. Cf. A118915, A247478, A253939.

%K nonn

%O 1,1

%A _Zak Seidov_, Jan 20 2015