A242115 Woodall semiprimes: Semiprimes of the form n*2^n - 1.

159, 895, 2047, 4607, 10239, 49151, 4718591, 20971519, 838860799, 137438953471, 5085241278463, 21440476741631, 340010386766614455386111, 96714065569170333976494079, 3288278229351791355200798719, 111414603535684224740921180159, 15370263527767281493147526365183

Offset: 1

Author

K. D. Bajpai, May 04 2014

Keywords

• nonn

Comments

The n-th Woodall number is Wn = n*2^n - 1.

If Wn is semiprime, it is in the sequence.

Examples

			a(1) = 159 = (5*2^5 - 1) is 5th Woodall number and 159 = 3*53 which is semiprime.
a(2) = 895 = (7*2^7 - 1) is 7th Woodall number and 895 = 5*179 which is semiprime.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..47 (terms 1..26 from K. D. Bajpai)

Crossrefs

Cf. A001358, A002234, A003261, A050918, A242273.

Programs

Maple

with(numtheory): A242115:= proc(); if bigomega(x*2^x-1)=2 then RETURN (x*2^x-1); fi; end: seq(A242115 (),x=1..200);

Mathematica

Select[Table[n*2^n-1,{n,100}],PrimeOmega[#]==2&] (* Harvey P. Dale, Jan 03 2019 *)

PARI

for(n=1, 1000, if(bigomega(n*2^n-1)==2, print1(n*2^n-1, ", "))) \\ Colin Barker, May 07 2014

Formula

a(n) = A003261(A242273(n)). - Amiram Eldar, Nov 27 2019