A309856 Primes of the form 2*p^3+1 where p is also prime.

17, 251, 2663, 48779, 410759, 715823, 2450087, 6615899, 13935743, 15290747, 23394167, 38930219, 160125983, 219804479, 236741543, 1258845587, 1666475243, 2116179719, 2308641299, 3604970627, 3991233959, 4283401139, 6109873703, 8207369603, 8487319319, 9264815927

Offset

1,1

Comments

All terms == 5 (mod 6).

Links

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

Formula

a(n) = 1+2*A309857(n)^3.

Maple

f:= proc(n) if isprime(n) and isprime(2*n^3+1) then return 2*n^3+1 fi end proc:
map(f, [2, seq(i, i=5..10000, 6)]); # Robert Israel, Aug 22 2019

Mathematica

pp = Join[{2}, Select[Range[5, 10000, 6], PrimeQ[#] && PrimeQ[2#^3 + 1]&]];
2 pp^3 + 1 (* Jean-François Alcover, Jul 31 2020 *)
Select[2*Prime[Range[300]]^3+1, PrimeQ] (* Harvey P. Dale, Dec 09 2024 *)

Crossrefs

Cf. A309857.

Subsequence of A214175 and of A201107.

Sequence in context: A294810 A362233 A214175 * A201302 A217453 A015675

Adjacent sequences: A309853 A309854 A309855 * A309857 A309858 A309859

Keyword

nonn

Author

R. J. Mathar, Aug 20 2019

Status

approved