login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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 (list; graph; refs; listen; history; text; internal format)
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

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

Sequence in context: A147405 A111440 A077118 * A209530 A147392 A147318

Adjacent sequences:  A242113 A242114 A242115 * A242117 A242118 A242119

KEYWORD

nonn

AUTHOR

K. D. Bajpai, May 04 2014

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 15 04:34 EDT 2020. Contains 335763 sequences. (Running on oeis4.)