A074184 Index of the smallest power of n >= n!.

1, 1, 2, 3, 3, 4, 5, 6, 6, 7, 8, 9, 9, 10, 11, 12, 12, 13, 14, 15, 15, 16, 17, 18, 19, 19, 20, 21, 22, 22, 23, 24, 25, 26, 26, 27, 28, 29, 30, 30, 31, 32, 33, 34, 34, 35, 36, 37, 38, 38, 39, 40, 41, 42, 43, 43, 44, 45, 46, 47, 47, 48, 49, 50, 51, 51, 52, 53, 54, 55, 56, 56, 57

Offset: 1

Author

Amarnath Murthy, Aug 31 2002

Keywords

• nonn
• easy

Comments

Essentially the same as A060151. - R. J. Mathar, Dec 15 2008

Links

• Danny Rorabaugh, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A039960, A074181, A074182.

Programs

Magma

[1] cat [Ceiling(Log(Factorial(n))/Log(n)): n in [2..80]]; // Vincenzo Librandi, Apr 15 2015

PARI

a(n)=if(n>2,lngamma(n+1)\log(n))+1 \\ Charles R Greathouse IV, Sep 02 2015

Sage

[1]+[ceil(log(factorial(n))/log(n)) for n in range(2, 74)] # Danny Rorabaugh, Apr 14 2015

Formula

From Danny Rorabaugh, Apr 14 2015: (Start)

a(n) = log_n(A074181(n)).

a(n) = ceiling(log_n(n!)) for n>1.

a(n) = A060151(n) = 1 + A039960(n) = 1 + log_n(A074182(n)) for n>2.

(End)

Extensions

More terms from Jason Earls, Sep 02 2002