A268110 Numbers k such that (2^k - k + 1)*2^k + 1 is a semiprime.

3, 4, 6, 9, 10, 15, 19, 22, 26, 34, 47, 55, 67, 69, 72, 92, 100, 117, 160, 169, 268, 278, 298, 309, 386, 430, 495

Offset

1,1

Links

Table of n, a(n) for n=1..27.

Example

a(1) = 3 because 6*8 + 1 = 49 = 7*7, which is semiprime.
a(2) = 4 because 13*16 + 1 = 209 = 11*19, which is semiprime.

Maple

A268110:=n->`if`(numtheory[bigomega]((2^n-n+1)*2^n+1)=2, n, NULL): seq(A268110(n), n=1..80); # Wesley Ivan Hurt, Jan 30 2016

Mathematica

Select[Range[105], PrimeOmega[(2^# - # + 1) 2^# + 1] == 2 &]

Prog

(Magma) IsSemiprime:=func<i | &+[d[2]: d in Factorization(i)] eq 2>; [n: n in [2..105]| IsSemiprime(s) where s is (2^n-n+1)*2^n+1];
(PARI) lista(nn) = {for(n=1, nn, if(bigomega((2^n-n+1)*2^n+1) == 2, print1(n, ", "))); } \\ Altug Alkan, Feb 07 2016

Crossrefs

Cf. A201360: n for which (2^n-n+1)*2^n+1 is prime.

Sequence in context: A245810 A054686 A005214 * A124093 A025061 A284741

Adjacent sequences: A268107 A268108 A268109 * A268111 A268112 A268113

Keyword

nonn,more

Author

Vincenzo Librandi, Jan 30 2016

Extensions

a(18)-a(19) from Daniel Suteu, Aug 05 2019

a(20)-a(27) from Tyler Busby, Feb 17 2023

Status

approved