A351988 In the factorial base expansion of n, arrange digits in decreasing order.

0, 1, 2, 3, 4, 5, 6, 8, 8, 9, 14, 15, 12, 14, 14, 15, 16, 17, 18, 20, 20, 21, 22, 23, 24, 30, 30, 32, 54, 56, 30, 32, 32, 33, 56, 57, 54, 56, 56, 57, 62, 63, 78, 80, 80, 81, 86, 87, 48, 54, 54, 56, 60, 62, 54, 56, 56, 57, 62, 63, 60, 62, 62, 63, 64, 65, 84, 86

Offset: 0

Author

Rémy Sigrist, Feb 27 2022

Keywords

• nonn
• base

Comments

This sequence is to factorial base what A004186 is to decimal base.

Examples

			For n = 1664:
- the factorial base expansion of 1664 is "214110",
- arranging these digits in decreasing order gives "421110",
- so a(1664) = 4*6! + 2*5! + 1*4! + 1*3! + 1*2! + 0*1! = 3152.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..5040
• Index entries for sequences related to factorial base representation

Crossrefs

Cf. A004186 (decimal analog), A073138 (binary analog), A108731, A319651 (ternary analog), A351987.

Programs

Mathematica

max = 5; b = MixedRadix[Range[max, 2, -1]]; a[n_] := FromDigits[Sort[IntegerDigits[n, b], Greater], b]; Array[a, max!, 0] (* Amiram Eldar, Feb 28 2022 *)

PARI

a(n) = { my (dd=[]); for (r=2, oo, if (n==0, dd = vecsort(dd); return (sum(k=1, #dd, dd[k]*k!)), dd = concat(dd, n%r); n\=r)) }

Formula

a(a(n)) = a(n).

a(n) >= n with equality iff n belongs to A351987.