A360994 Numbers k such that (2^k + 1)^3 - 2 is a semiprime.

0, 1, 2, 4, 5, 6, 13, 14, 18, 27, 43, 45, 63, 76, 85, 108, 115, 119, 123, 187, 211, 215, 283, 312

Offset: 1

Author

Serge Batalov, Feb 27 2023

Keywords

• nonn
• more
• hard

Comments

a(25) >= 355.

623, 674, 711, 766, 767 are also in this sequence, but their position cannot be established before finding any factor for the values corresponding to the following "blockers": 355, 511, 587, 707, 731.

1424, 1470, 1580, 1946, 2117, 2693, 3000, 3540, 4164, 7043, 9475, 10632, 15018, 19064, 27130, 28266, 28532, 46434, 58768, 103536 are some larger members of this sequence, but their position cannot be established. These produce "trivial" semiprimes where one prime is small (e.g., 3 or 5).

Links

• factordb.com, Status of (2^355+1)^3-2.

Crossrefs

Cf. A001358, A091513, A091514, A093069, A099359, A100899, A100900, A269264, A360993.

Programs

Magma

IsSemiprime:=func; [n: n in [1..70]| IsSemiprime(s) where s is (2^n+1)^3-2];

Mathematica

Select[Range[70], PrimeOmega[(2^# + 1)^3 - 2] == 2 &]

PARI

isok(n) = bigomega((2^n+1)^3-2) == 2;

Formula

{ k >= 0 : A099359(k) in { A001358 } }.