A119564 Define F(n) = 2^(2^n)+1 = n-th Fermat number, M(n) = 2^n-1 = the n-th Mersenne number. Then a(n) = F(n)-M(n)-1 = 2^(2^n) - 2^n + 1.

2, 3, 13, 249, 65521, 4294967265, 18446744073709551553, 340282366920938463463374607431768211329, 115792089237316195423570985008687907853269984665640564039457584007913129639681

Offset: 0

Author

Cino Hilliard, May 31 2006

Keywords

• nonn

Comments

The numbers n that divide a(n) are A373580. - Thomas Ordowski, Jun 11 2024

Examples

			F(2) = 2^(2^2)+1 = 17, M(2) = 2^2-1 = 3, F(2)-M(2)-1 = 13.
		

Crossrefs

Cf. A119550, A119563, A307843, A373580.

Programs

PARI

fm4(n) = for(x=0,n,y=2^(2^x)+1-(2^x-1)-1;print1(y","))

Formula

a(n) = (2^(2^n) - 1) - (2^n - 2). - Thomas Ordowski, Jun 11 2024

Extensions

Edited by N. J. A. Sloane, Jun 03 2006

Definition corrected by R. J. Mathar, May 15 2007