A246359 - OEIS

%I #29 Mar 24 2021 09:52:04

%S 0,1,1,1,2,2,1,1,1,1,2,2,2,2,2,2,2,2,3,3,3,3,3,3,1,1,1,1,2,2,1,1,1,1,

%T 2,2,2,2,2,2,2,2,3,3,3,3,3,3,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,

%U 3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4

%N Maximum digit in the factorial base expansion of n (A007623).

%C Maximum entry in n-th row of A108731.

%H Antti Karttunen, <a href="/A246359/b246359.txt">Table of n, a(n) for n = 0..10080</a>

%H <a href="/index/Fa#facbase">Index entries for sequences related to factorial base representation</a>

%F From _Antti Karttunen_, Aug 29 2016: (Start)

%F a(0) = 0; for n >= 1, a(n) = 1 + a(A257684(n)).

%F a(0) = 0; for n >= 1, a(n) = max(A099563(n), a(A257687(n))).

%F a(n) = A051903(A276076(n)).

%F (End)

%e Factorial base representation of 46 is "1320" as 46 = 1*4! + 3*3! + 2*2! + 0*1!, and the largest of these digits is 3, thus a(46) = 3.

%t nn = 96; m = 1; While[Factorial@ m < nn, m++]; m; Table[Max@ IntegerDigits[n, MixedRadix[Reverse@ Range[2, m]]], {n, 0, nn}] (* Version 10.2, or *)

%t f[n_] := Block[{a = {{0, n}}}, Do[AppendTo[a, {First@ #, Last@ #} &@ QuotientRemainder[a[[-1, -1]], Times @@ Range[# - i]]], {i, 0, #}] &@ NestWhile[# + 1 &, 0, Times @@ Range[# + 1] <= n &]; Most@ Rest[a][[All, 1]] /. {} -> {0}]; Table[Max@ f@ n, {n, 0, 96}] (* _Michael De Vlieger_, Aug 29 2016 *)

%o (MIT/GNU Scheme) (define (A246359 n) (let loop ((n n) (i 2) (md 0)) (if (zero? n) md (loop (floor->exact (/ n i)) (+ i 1) (max (modulo n i) md)))))

%o (Python)

%o def a007623(n, p=2): return n if n<p else a007623(n//p, p+1)*10 + n%p

%o def a(n): return int(max(str(a007623(n))))

%o print([a(n) for n in range(101)]) # _Indranil Ghosh_, Jun 21 2017

%Y Cf. A007623, A034968, A051903, A060130, A084558, A099563, A257684, A257687, A276076.

%Y Cf. also A249070.

%K nonn,base

%O 0,5

%A _Antti Karttunen_, Oct 20 2014