A242116 Cullen semiprimes: Semiprimes of the form k*2^k + 1.

9, 25, 65, 161, 2049, 4609, 22529, 1048577, 44040193, 283467841537, 1202590842881, 256065421246102339102334047485953, 4259306016766850789028922770063361, 356615920533143509709616588588493085605889, 57729314674570665269045550892293179276409335447553

Offset: 1

Author

K. D. Bajpai, May 04 2014

Keywords

• nonn

Comments

The k-th Cullen number Cullen(k) = k*2^k + 1.

If Cullen(k) is semiprime, it is in the sequence.

The next term, a(16), has 52 digits.

Examples

			a(4) = 161 = (5*2^5+1) is 5th Cullen number and 161 = 7 * 23 is semiprime.
a(5) = 2049 = (8*2^8+1) is 8th Cullen number and 2049 = 3 * 683 is semiprime.
		

Links

• Tyler Busby, Table of n, a(n) for n = 1..35 (terms 1..16 from K. D. Bajpai, terms 17..34 from Amiram Eldar)

Crossrefs

Cf. A001358, A002064, A003261, A005849, A242175.

Programs

Magma

IsSemiprime:=func; [s: n in [1..200] | IsSemiprime(s) where s is n*2^n+1]; // // Vincenzo Librandi, May 07 2014

Maple

with(numtheory): A242116:= proc(); if bigomega(x*2^x+1) = 2 then RETURN (x*2^x+1);  fi; end: seq(A242116 (), x=1..200);

Mathematica

cullen[n_] := n * 2^n + 1; Select[cullen[Range[35]], PrimeOmega[#] == 2 &] (* Amiram Eldar, Nov 27 2019 *)

PARI

select(n->bigomega(n)==2, vector(90,n,n<Charles R Greathouse IV, May 06 2014

Formula

a(n) = A002064(A242175(n)). - Amiram Eldar, Nov 27 2019