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A342116
Lexicographically latest sequence of distinct nonnegative integers such that the multisets of frequencies of digits in the factorial base representations of n and of a(n) are the same.
2
0, 1, 5, 3, 4, 2, 21, 18, 17, 9, 23, 16, 15, 22, 20, 12, 11, 8, 7, 19, 14, 6, 13, 10, 105, 93, 90, 96, 117, 114, 63, 81, 72, 33, 113, 65, 112, 111, 108, 64, 107, 60, 104, 103, 102, 57, 119, 100, 48, 99, 98, 97, 59, 95, 94, 92, 91, 45, 89, 52, 41, 88, 87, 30
OFFSET
0,3
COMMENTS
This sequence is a self-inverse permutation of the nonnegative integers.
FORMULA
a(n) < k! for any n < k!.
a(A007489(n)) = A007489(n).
EXAMPLE
The first terms, in decimal and in factorial base, alongside the corresponding multisets of frequencies (ignoring 0's), are:
n a(n) fact(n) fact(a(n)) freq(n)
-- ---- ------- ---------- ------------
0 0 0 0 ()
1 1 1 1 (1)
2 5 10 21 (1, 1)
3 3 11 11 (2)
4 4 20 20 (1, 1)
5 2 21 10 (1, 1)
6 21 100 311 (1, 2)
7 18 101 300 (1, 2)
8 17 110 221 (1, 2)
9 9 111 111 (3)
10 23 120 321 (1, 1, 1)
11 16 121 220 (1, 2)
12 15 200 211 (1, 2)
PROG
(PARI) See Links section.
CROSSREFS
See A342102 for similar sequences.
Sequence in context: A243359 A222229 A168360 * A342117 A107488 A114236
KEYWORD
nonn,base
AUTHOR
Rémy Sigrist, Feb 28 2021
STATUS
approved