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A343506
Numbers k such that the largest digit in the factorial base expansion of 1/k is 1.
0
1, 2, 6, 20, 24, 120, 630, 720, 4480, 5040, 36288, 40320, 362880, 3326400, 3628800, 39916800
OFFSET
1,2
COMMENTS
Equivalently these are the numbers k such that A299020(k) = 1 or A343505(k) = 1.
This sequence is infinite as it contains:
- the factorial numbers (A000142),
- 1/(1/A060462(k)! + 1/(A060462(k)-1)!) for k > 2,
- 1/(1/A120416(k)! + 1/(A120416(k)-1)! + 1/(A120416(k)-2)!) for k > 0.
EXAMPLE
The first terms, alongside the factorial base expansion of their inverse, are:
n a(n) 1/a(n) in factorial base
-- ------- ------------------------
1 1 1
2 2 0.1
3 6 0.0 1
4 20 0.0 0 1 1
5 24 0.0 0 1
6 120 0.0 0 0 1
7 630 0.0 0 0 0 1 1
8 720 0.0 0 0 0 1
9 4480 0.0 0 0 0 0 1 1
10 5040 0.0 0 0 0 0 1
11 36288 0.0 0 0 0 0 0 1 1
12 40320 0.0 0 0 0 0 0 1
13 362880 0.0 0 0 0 0 0 0 1
14 3326400 0.0 0 0 0 0 0 0 0 1 1
15 3628800 0.0 0 0 0 0 0 0 0 1
PROG
(PARI) is(n) = my (f=1/n); for (r=2, oo, if (f==0, return (1), floor(f)>1, return (0), f=frac(f)*r))
CROSSREFS
Cf. A333402 (decimal).
Sequence in context: A156269 A370974 A370968 * A128447 A032622 A104749
KEYWORD
nonn,base,more
AUTHOR
Rémy Sigrist, Apr 17 2021
STATUS
approved