A356585
Number of decimal digits in the n-th Gosper hyperfactorial of n (A330716).
Original entry on oeis.org
1, 1, 2, 16, 198, 2927, 50060, 979361, 21645853, 534381060, 14590180163, 436814197446, 14235563000269, 501817445873045, 19029286646922723, 772532087068933899, 33434018751249535666, 1536767964161539414904, 74769012084248550773909
Offset: 0
a(0)=1 since the 0th Gosper hyperfactorial (0!) has one decimal digit.
a(3)=16 since the 3rd Gosper hyperfactorial of 3 is 1952152956156672.
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Floor[Table[1+Sum[Log10[k]*(k^n), {k, 1, n}], {n, 1, 18}]]
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a(n) = floor(sum(k=1, n, log(k)*k^n/log(10))) + 1; \\ Michel Marcus, Sep 27 2022
A356586
Number of binary digits in the n-th Gosper hyperfactorial of n (A330716).
Original entry on oeis.org
1, 1, 5, 51, 657, 9722, 166296, 3253365, 71905965, 1775175455, 48467529392, 1451065354742, 47289516677131, 1667001471950287, 63213921938077523, 2566296044236261518, 111065406214766719510, 5105032675471072965466, 248377281869637961805657
Offset: 0
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.
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Floor[Table[1+Sum[Log[k]*(k^n)/Log[2], {k, 1, n}], {n, 1, 18}]]
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a(n) = floor(sum(k=1, n, log(k)*k^n/log(2))) + 1; \\ Michel Marcus, Sep 27 2022
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