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A242116
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Cullen semiprimes: Semiprimes of the form n*2^n + 1.
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2
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9, 25, 65, 161, 2049, 4609, 22529, 1048577, 44040193, 283467841537, 1202590842881, 256065421246102339102334047485953, 4259306016766850789028922770063361, 356615920533143509709616588588493085605889, 57729314674570665269045550892293179276409335447553
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OFFSET
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1,1
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COMMENTS
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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.
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LINKS
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FORMULA
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EXAMPLE
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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.
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MAPLE
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with(numtheory): A242116:= proc(); if bigomega(x*2^x+1) = 2 then RETURN (x*2^x+1); fi; end: seq(A242116 (), x=1..200);
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MATHEMATICA
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cullen[n_] := n * 2^n + 1; Select[cullen[Range[35]], PrimeOmega[#] == 2 &] (* Amiram Eldar, Nov 27 2019 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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