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A356586
Number of binary digits in the n-th Gosper hyperfactorial of n (A330716).
1
1, 1, 5, 51, 657, 9722, 166296, 3253365, 71905965, 1775175455, 48467529392, 1451065354742, 47289516677131, 1667001471950287, 63213921938077523, 2566296044236261518, 111065406214766719510, 5105032675471072965466, 248377281869637961805657
OFFSET
0,3
COMMENTS
The 0th Gosper hyperfactorial is the usual factorial function.
FORMULA
a(n) = A070939(A330716(n)).
EXAMPLE
a(0)=1 since 0! has 1 binary digit.
a(3)=51 since the 3rd Gosper hyperfactorial of 3 in binary is 110111011110111100100000111011111111011101100000000, which has 51 digits.
MATHEMATICA
Floor[Table[1+Sum[Log[k]*(k^n)/Log[2], {k, 1, n}], {n, 1, 18}]]
PROG
(PARI) a(n) = floor(sum(k=1, n, log(k)*k^n/log(2))) + 1; \\ Michel Marcus, Sep 27 2022
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Greg Huber, Aug 13 2022
STATUS
approved