VOOZH about

URL: https://oeis.org/A389644

⇱ A389644 - OEIS

login
A389644
Nonnegative numbers k such that for some integer m the factorial base expansion of k (without leading zeros), when read backwards, corresponds to that of m, and conversely, the factorial base expansion of m (without leading zeros), when read backwards, corresponds to that of k.
3
0, 1, 3, 7, 9, 11, 25, 27, 29, 31, 33, 35, 37, 39, 41, 121, 123, 125, 127, 129, 131, 133, 135, 137, 139, 141, 143, 145, 147, 149, 151, 153, 155, 157, 159, 161, 163, 165, 167, 169, 171, 173, 175, 177, 179, 181, 183, 185, 187, 189, 191, 721, 723, 725, 727, 729
OFFSET
1,3
COMMENTS
This sequence naturally contains the palindromes in factorial base (A046807).
A positive number k belongs to this sequence iff its factorial base expansion, say (d_1, ..., d_w), satisfies d_1 = d_w = 1 and d_i <= i for i in 1..w.
There are A010551(w+2)/4 terms with w digits in factorial base for w > 1.
EXAMPLE
The first terms, alongside their factorial base expansion, are:
n a(n) fact(a(n))
-- ---- -----------
1 0 ()
2 1 (1)
3 3 (1,1)
4 7 (1,0,1)
5 9 (1,1,1)
6 11 (1,2,1)
7 25 (1,0,0,1)
8 27 (1,0,1,1)
9 29 (1,0,2,1)
10 31 (1,1,0,1)
11 33 (1,1,1,1)
12 35 (1,1,2,1)
13 37 (1,2,0,1)
14 39 (1,2,1,1)
15 41 (1,2,2,1)
16 121 (1,0,0,0,1)
17 123 (1,0,0,1,1)
18 125 (1,0,0,2,1)
PROG
(PARI) \\ See Links section.
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Rémy Sigrist, Oct 09 2025
STATUS
approved