A246359 Maximum digit in the factorial base expansion of n (A007623).

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, 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, 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

Offset: 0

Author

Antti Karttunen, Oct 20 2014

Keywords

• nonn
• base

Comments

Maximum entry in n-th row of A108731.

Examples

			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.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 0..10080
• Index entries for sequences related to factorial base representation

Crossrefs

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

Cf. also A249070.

Programs

Mathematica

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 *)
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 *)

Python

def a007623(n, p=2): return n if n
Indranil Ghosh, Jun 21 2017

Formula

From Antti Karttunen, Aug 29 2016: (Start)

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

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

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

(End)