A094331 -id:A094331 - cp's OEIS frontend

A075357 a(n) = smallest k such that (n+1)(n+2)...(n+k) >= n!.

0, 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

Offset: 1

Amarnath Murthy, Sep 19 2002

nonn

Is this sequence the same as A094331? - David Wasserman, Jan 16 2005

Michael S. Branicky, Table of n, a(n) for n = 1..10000

Cf. A075358.

Cf. A094331.

a(n) = my(k=0); while ((n+k)! < n!^2, k++); k; \\ Michel Marcus, Apr 11 2022

from math import factorial
def a(n):
    if n == 1: return 0
    fn, k, p = factorial(n), 1, n+1
    while fn > p: k += 1; p *= (n+k)
    return k
print([a(n) for n in range(1, 75)]) # Michael S. Branicky, Apr 11 2022

More terms from David Wasserman, Jan 16 2005

A213854 Least m>0 such that m!*3^m >= n!.

Original entry on oeis.org

1, 1, 2, 3, 3, 4, 5, 6, 6, 7, 8, 9, 9, 10, 11, 12, 13, 13, 14, 15, 16, 17, 17, 18, 19, 20, 21, 21, 22, 23, 24, 25, 25, 26, 27, 28, 29, 29, 30, 31, 32, 33, 34, 34, 35, 36, 37, 38, 38, 39, 40, 41, 42, 43, 43, 44, 45, 46, 47, 48, 48, 49, 50

Offset: 1

Clark Kimberling, Jul 17 2012

			a(6) = 4 because 3^3*3! < 6! <= 3^4*4!.

Clark Kimberling, Table of n, a(n) for n = 1..1000

Cf. A094331, A213851.

A213854 := proc(n)
        for m from 1 do
                if (3^m)*m! >= n! then
                        return m;
                end if;
        end do:
end proc: # R. J. Mathar, Jul 18 2012

Table[m=1; While[n!>(3^m)*m!, m++]; m, {n,1,100}]
With[{tbl=Table[m! 3^m,{m,60}]},Table[Position[tbl,?(#>n!&),1,1],{n,70}]]//Flatten (* _Harvey P. Dale, Jun 08 2024 *)

A213851 Least m such that m!*2^m >= n!

Original entry on oeis.org

1, 1, 2, 3, 4, 5, 6, 6, 7, 8, 9, 10, 11, 12, 12, 13, 14, 15, 16, 17, 18, 18, 19, 20, 21, 22, 23, 24, 24, 25, 26, 27, 28, 29, 30, 31, 31, 32, 33, 34, 35, 36, 37, 38, 38, 39, 40, 41, 42, 43, 44, 45, 46, 46, 47, 48, 49, 50, 51, 52, 53, 53, 54

Offset: 1

Clark Kimberling, Jul 17 2012

			a(8) = 6 because (2^5)*5! < 8! <= (2^6)*6!.

Clark Kimberling, Table of n, a(n) for n = 1..1000

Cf. A094331.

Table[m=1; While[n!>(2^m)*m!, m++]; m, {n,1,100}]

cp's OEIS Frontend

A075357 a(n) = smallest k such that (n+1)(n+2)...(n+k) >= n!.

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A213854 Least m>0 such that m!*3^m >= n!.

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Maple

Mathematica

A213851 Least m such that m!*2^m >= n!

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Mathematica