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

0,3

Comments

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

Links

Rémy Sigrist, Table of n, a(n) for n = 0..5040

Index entries for sequences related to factorial base representation

Formula

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

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

Example

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.

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 *)

Prog

(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)) }

Crossrefs

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

Sequence in context: A210253 A130916 A003965 * A214964 A097502 A318122

Adjacent sequences: A351985 A351986 A351987 * A351989 A351990 A351991

Keyword

nonn,base

Author

Rémy Sigrist, Feb 27 2022

Status

approved