cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A090620 Highest power of 13 dividing n!.

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%I A090620 #19 Jun 20 2020 16:10:35
%S A090620 0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,
%T A090620 2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,
%U A090620 5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,8
%N A090620 Highest power of 13 dividing n!.
%H A090620 Alois P. Heinz, <a href="/A090620/b090620.txt">Table of n, a(n) for n = 0..10000</a> (first 1001 terms from T. D. Noe)
%F A090620 a(n) = A090622(n, 13) = A090623(n, 13) = [n/13]+[n/169]+[n/2197]+...
%F A090620 a(n) = n/12 + O(log n). - _Charles R Greathouse IV_, Aug 06 2012
%p A090620 a:= proc(n) option remember; `if`(n=0, 0,
%p A090620       a(n-1)+padic[ordp](n, 13))
%p A090620     end:
%p A090620 seq(a(n), n=0..120);  # _Alois P. Heinz_, Jun 20 2020
%t A090620 IntegerExponent[Range[0,110]!,13] (* _Harvey P. Dale_, Aug 22 2011 *)
%t A090620 FoldList[Plus, 0, IntegerExponent[Range[100], 13]] (* _T. D. Noe_, Apr 10 2012 *)
%o A090620 (PARI) a(n)=my(t);while(n,t+=n\=13);t \\ _Charles R Greathouse IV_, Aug 06 2012
%Y A090620 Cf. A011371, A054861.
%K A090620 nonn,easy
%O A090620 0,27
%A A090620 _Henry Bottomley_, Dec 06 2003