A264688 Numbers k such the digits of k appear k times in total in the decimal representation of k!.

0, 1, 1170, 1528, 9877, 9886, 9897, 11535

Offset

1,3

Comments

There are no more terms up to k = 21000, checked using the Python program below.

a(9) > 200000. - Dana Jacobsen, Jan 03 2016

a(9) > 1000000. - Michael S. Branicky, Feb 04 2026

Links

Table of n, a(n) for n=1..8.

Example

1170 belongs to this sequence because the digits 1, 7 and 0 appear 1170 times in total in the decimal representation of 1170!.
0! = 1, which contains no zeros, so 0 is a term.

Prog

(Python)
from math import factorial
def in_a(n):
    f = str(factorial(n))
    s = set(str(n))
    return sum(f.count(d) for d in s)==n
(Python)
from collections import Counter
from gmpy2 import digits, fac, mpz
def ok(k):
    c = Counter(digits(fac(mpz(k))))
    return sum(c[d] for d in set(digits(k))) == k
print([k for k in range(12000) if ok(k)]) # Michael S. Branicky, Feb 04 2026
(Perl) use ntheory ":all"; sub is_a264688 { my $n = shift; $n == eval "factorial($n) =~ tr/[$n]//"; } # Dana Jacobsen, Jan 03 2016

Crossrefs

Sequence in context: A065656 A185468 A209825 * A043432 A065703 A202487

Adjacent sequences: A264685 A264686 A264687 * A264689 A264690 A264691

Keyword

nonn,base,more

Author

Christian Perfect, Jan 03 2016

Status

approved