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A094331
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Least k such that n! < (n+1)(n+2)(n+3)...(n+k).
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4
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1, 1, 2, 2, 3, 4, 4, 5, 6, 6, 7, 8, 8, 9, 10, 11, 11, 12, 13, 13, 14, 15, 16, 16, 17, 18, 18, 19, 20, 21, 21, 22, 23, 24, 24, 25, 26, 27, 27, 28, 29, 30, 30, 31, 32, 33, 33, 34, 35, 36, 37, 37, 38, 39, 40, 40, 41, 42, 43, 43, 44, 45, 46, 47, 47, 48, 49, 50, 50, 51, 52, 53, 53, 54
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OFFSET
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1,3
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LINKS
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FORMULA
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a(n) = f(n) + 1, where f(n) is the function defined on p. 65 of Brilleslyper et al. - Michel Marcus, Apr 11 2022
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MATHEMATICA
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lk[n_]:=Module[{k=1, f=n!}, While[f>=Times@@Table[n+i, {i, k}], k++]; k]; Array[lk, 80] (* Harvey P. Dale, Sep 20 2016 *)
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PROG
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(PARI) a(n) = my(k=0); while (n!^2 >= (n+k)!, k++); k; \\ Michel Marcus, Apr 11 2022
(Python)
from math import factorial
def a(n):
fn, k, p = factorial(n), 1, n+1
while fn >= p: k += 1; p *= (n+k)
return k
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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