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

%I

%S 9,25,65,161,2049,4609,22529,1048577,44040193,283467841537,

%T 1202590842881,256065421246102339102334047485953,

%U 4259306016766850789028922770063361,356615920533143509709616588588493085605889,57729314674570665269045550892293179276409335447553

%N Cullen semiprimes: Semiprimes of the form n*2^n + 1.

%C The n-th Cullen number Cullen(n) = n*2^n + 1.

%C If Cullen(n) is semiprime, it is in the sequence.

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

%H Amiram Eldar, <a href="/A242116/b242116.txt">Table of n, a(n) for n = 1..34</a> (terms 1..16 from K. D. Bajpai)

%F a(n) = A002064(A242175(n)). - _Amiram Eldar_, Nov 27 2019

%e a(4) = 161 = (5*2^5+1) is 5th Cullen number and 161 = 7 * 23 is semiprime.

%e a(5) = 2049 = (8*2^8+1) is 8th Cullen number and 2049 = 3 * 683 is semiprime.

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

%t cullen[n_] := n * 2^n + 1; Select[cullen[Range], PrimeOmega[#] == 2 &] (* _Amiram Eldar_, Nov 27 2019 *)

%o (PARI) select(n->bigomega(n)==2, vector(90,n,n<<n+1)) \\ _Charles R Greathouse IV_, May 06 2014

%o (MAGMA) IsSemiprime:=func<i | &+[d: 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

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

%K nonn

%O 1,1

%A _K. D. Bajpai_, May 04 2014

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Last modified August 4 09:03 EDT 2020. Contains 336201 sequences. (Running on oeis4.)