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%I #16 Dec 09 2024 15:07:40
%S 17,251,2663,48779,410759,715823,2450087,6615899,13935743,15290747,
%T 23394167,38930219,160125983,219804479,236741543,1258845587,
%U 1666475243,2116179719,2308641299,3604970627,3991233959,4283401139,6109873703,8207369603,8487319319,9264815927
%N Primes of the form 2*p^3+1 where p is also prime.
%C All terms == 5 (mod 6).
%H Robert Israel, <a href="/A309856/b309856.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = 1+2*A309857(n)^3.
%p f:= proc(n) if isprime(n) and isprime(2*n^3+1) then return 2*n^3+1 fi end proc:
%p map(f, [2,seq(i,i=5..10000,6)]);# _Robert Israel_, Aug 22 2019
%t pp = Join[{2}, Select[Range[5, 10000, 6], PrimeQ[#] && PrimeQ[2#^3 + 1]&]];
%t 2 pp^3 + 1 (* _Jean-François Alcover_, Jul 31 2020 *)
%t Select[2*Prime[Range[300]]^3+1,PrimeQ] (* _Harvey P. Dale_, Dec 09 2024 *)
%Y Cf. A309857.
%Y Subsequence of A214175 and of A201107.
%K nonn
%O 1,1
%A _R. J. Mathar_, Aug 20 2019