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A242116
Cullen semiprimes: Semiprimes of the form n*2^n + 1.
2
9, 25, 65, 161, 2049, 4609, 22529, 1048577, 44040193, 283467841537, 1202590842881, 256065421246102339102334047485953, 4259306016766850789028922770063361, 356615920533143509709616588588493085605889, 57729314674570665269045550892293179276409335447553
OFFSET
1,1
COMMENTS
The n-th Cullen number Cullen(n) = n*2^n + 1.
If Cullen(n) is semiprime, it is in the sequence.
The next term, a(16), has 52 digits.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..34 (terms 1..16 from K. D. Bajpai)
FORMULA
a(n) = A002064(A242175(n)). - Amiram Eldar, Nov 27 2019
EXAMPLE
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.
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 *)
PROG
(PARI) select(n->bigomega(n)==2, vector(90, n, n<<n+1)) \\ Charles R Greathouse IV, May 06 2014
(Magma) IsSemiprime:=func<i | &+[d[2]: d in Factorization(i)] eq 2>; [s: n in [1..200] | IsSemiprime(s) where s is n*2^n+1]; // // Vincenzo Librandi, May 07 2014
CROSSREFS
KEYWORD
nonn
AUTHOR
K. D. Bajpai, May 04 2014
STATUS
approved