A119564 - OEIS

%I #22 Jun 30 2024 20:58:42

%S 2,3,13,249,65521,4294967265,18446744073709551553,

%T 340282366920938463463374607431768211329,

%U 115792089237316195423570985008687907853269984665640564039457584007913129639681

%N 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.

%C The numbers n that divide a(n) are A373580. - _Thomas Ordowski_, Jun 11 2024

%F a(n) = (2^(2^n) - 1) - (2^n - 2). - _Thomas Ordowski_, Jun 11 2024

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

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

%Y Cf. A119550, A119563, A307843, A373580.

%K nonn

%O 0,1

%A _Cino Hilliard_, May 31 2006

%E Edited by _N. J. A. Sloane_, Jun 03 2006

%E Definition corrected by _R. J. Mathar_, May 15 2007