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

0,1

Comments

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

Links

Table of n, a(n) for n=0..8.

Formula

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

Example

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

Prog

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

Crossrefs

Cf. A119550, A119563, A307843, A373580.

Sequence in context: A056806 A376058 A270403 * A132358 A090100 A270314

Adjacent sequences: A119561 A119562 A119563 * A119565 A119566 A119567

Keyword

nonn

Author

Cino Hilliard, May 31 2006

Extensions

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

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

Status

approved