A356586 - OEIS

%I #29 Nov 19 2022 21:18:28

%S 1,1,5,51,657,9722,166296,3253365,71905965,1775175455,48467529392,

%T 1451065354742,47289516677131,1667001471950287,63213921938077523,

%U 2566296044236261518,111065406214766719510,5105032675471072965466,248377281869637961805657

%N Number of binary digits in the n-th Gosper hyperfactorial of n (A330716).

%C The 0th Gosper hyperfactorial is the usual factorial function.

%F a(n) = A070939(A330716(n)).

%e a(0)=1 since 0! has 1 binary digit.

%e a(3)=51 since the 3rd Gosper hyperfactorial of 3 in binary is 110111011110111100100000111011111111011101100000000, which has 51 digits.

%t Floor[Table[1+Sum[Log[k]*(k^n)/Log[2], {k, 1, n}], {n, 1, 18}]]

%o (PARI) a(n) = floor(sum(k=1, n, log(k)*k^n/log(2))) + 1; \\ _Michel Marcus_, Sep 27 2022

%Y Cf. A070939, A330716, A356585.

%K nonn,base

%O 0,3

%A _Greg Huber_, Aug 13 2022