A269264 Numbers k such that (2^k-1)^2 - 2 is a semiprime.

5, 9, 13, 16, 23, 24, 28, 35, 37, 38, 40, 47, 48, 51, 52, 57, 61, 65, 67, 70, 79, 83, 84, 85, 88, 90, 102, 111, 144, 148, 157, 162, 168, 169, 177, 181, 190, 237, 246, 298, 308, 346

Offset

1,1

Comments

a(43) >= 385. - Serge Batalov, Feb 26 2023

Links

Table of n, a(n) for n=1..42.

factordb.com, Status of (2^385-1)^2-2.

Example

a(1) = 5 because 31^2-2 = 959 = 7*137 which is semiprime.
a(2) = 9 because 511^2-2 = 261119 = 23*11353 which is semiprime.

Mathematica

Select[Range[120], PrimeOmega[(2^# - 1)^2 - 2] == 2 &]

Prog

(Magma) IsSemiprime:=func<i | &+[d[2]: d in Factorization(i)] eq 2>; [n: n in [2..120]| IsSemiprime(s) where s is (2^n-1)^2-2];
(PARI) isok(n) = bigomega((2^n-1)^2-2) == 2; \\ Michel Marcus, Feb 22 2016

Crossrefs

Cf. A091515, A091516, A268574, A360993, A360994.

Sequence in context: A281582 A190696 A314662 * A314663 A314664 A051541

Adjacent sequences: A269261 A269262 A269263 * A269265 A269266 A269267

Keyword

nonn,more,hard

Author

Vincenzo Librandi, Feb 21 2016

Extensions

a(29)-a(42) from Hugo Pfoertner, Aug 05 2019

Status

approved