A230506 Numbers n with 2*n + 1 and 2*n^3 + 1 both prime.

1, 2, 5, 6, 9, 11, 20, 21, 26, 29, 30, 35, 44, 86, 95, 96, 99, 111, 120, 134, 140, 165, 186, 191, 204, 221, 231, 249, 260, 299, 321, 330, 354, 375, 380, 384, 386, 431, 440, 455, 485, 491, 506, 515, 545, 551, 554, 596, 600, 629

Offset

1,2

Comments

This sequence is interesting because of the conjecture in the comments in A230507.

Links

Zhi-Wei Sun, Table of n, a(n) for n = 1..10000

Example

a(1) = 1 since 2*1 + 1 = 2*1^3 + 1 = 3 is a prime.
a(2) = 2 since 2*2 + 1 = 5 and 2*2^3 + 1 = 17 are both prime.

Mathematica

q[n_]:=PrimeQ[2n+1]&&PrimeQ[2n^3+1]
m=0
Do[If[q[n], m=m+1; Print[m, " ", n]], {n, 1, 629}]

Crossrefs

Cf. A000040, A005097, A201107, A230507.

Sequence in context: A024516 A286341 A284657 * A236072 A055938 A190764

Adjacent sequences: A230503 A230504 A230505 * A230507 A230508 A230509

Keyword

nonn

Author

Zhi-Wei Sun, Oct 21 2013

Status

approved