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%I #6 Oct 01 2013 17:58:25
%S 4,5,15,251,65523,4294967267,18446744073709551555,
%T 340282366920938463463374607431768211331,
%U 115792089237316195423570985008687907853269984665640564039457584007913129639683
%N Let F(n) = 2^(2^n) + 1 = the 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) + 1 - (2^n - 1) + 1 = 2^(2^n) - 2^n + 3.
%F a(n) = A001146(n)-A000079(n)+3 = A119564(n)+2. - _R. J. Mathar_, May 15 2007
%e F(1) = 2^(2^1)+1 = 5
%e M(1) = 2^1-1 = 1
%e F(1) - M(2) + 1 = 5
%o (PARI) fm2(n) = for(x=0,n,y=2^(2^x)-2^x+3;print1(y","))
%K nonn
%O 0,1
%A _Cino Hilliard_, May 31 2006
%E Definition corrected by _R. J. Mathar_, May 15 2007
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