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Index of the smallest power of n >= n!.
8

%I #22 Sep 08 2022 08:45:07

%S 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,

%T 21,22,22,23,24,25,26,26,27,28,29,30,30,31,32,33,34,34,35,36,37,38,38,

%U 39,40,41,42,43,43,44,45,46,47,47,48,49,50,51,51,52,53,54,55,56,56,57

%N Index of the smallest power of n >= n!.

%C Essentially the same as A060151. - _R. J. Mathar_, Dec 15 2008

%H Danny Rorabaugh, <a href="/A074184/b074184.txt">Table of n, a(n) for n = 1..10000</a>

%F From _Danny Rorabaugh_, Apr 14 2015: (Start)

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

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

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

%F (End)

%o (Sage) [1]+[ceil(log(factorial(n))/log(n)) for n in range(2, 74)] # _Danny Rorabaugh_, Apr 14 2015

%o (Magma) [1] cat [Ceiling(Log(Factorial(n))/Log(n)): n in [2..80]]; // _Vincenzo Librandi_, Apr 15 2015

%o (PARI) a(n)=if(n>2,lngamma(n+1)\log(n))+1 \\ _Charles R Greathouse IV_, Sep 02 2015

%Y Cf. A039960, A074181, A074182.

%K nonn,easy

%O 1,3

%A _Amarnath Murthy_, Aug 31 2002

%E More terms from _Jason Earls_, Sep 02 2002