A360181 Numbers k such that the number of odd digits in k! is greater than or equal to the number of even digits.

0, 1, 11, 29, 36, 193, 281

Offset

1,3

Comments

If it exists, a(8) > 100000.

Links

Table of n, a(n) for n=1..7.

Example

11 is a term since 11! = 39916800, and the numbers of odd and even digits are both 4.
29 is a term since 29!=8841761993739701954543616000000, and the numbers of odd and even digits are 16 and 15 respectively.

Mathematica

Select[Range[0, 500],
 Count[IntegerDigits[#!], _?OddQ] >=
   Count[IntegerDigits[#!], _?EvenQ] &]

Prog

(Python)
from sympy import factorial as f
def ok(n):
    s=str(f(n))
    return(sum(1 for k in s if k in '02468')<=sum(1 for k in s if k in '13579'))
print([n for n in range(501) if ok(n)])
(Python)
from math import factorial
from itertools import count, islice
def A360181_gen(startvalue=0): # generator of terms >= startvalue
    f = factorial(m:=max(startvalue, 0))
    for k in count(m):
        if len(s:=str(f)) <= sum(1 for d in s if d in {'1', '3', '5', '7', '9'})<<1:
            yield k
        f *= k+1
A360181_list = list(islice(A360181_gen(), 7)) # Chai Wah Wu, May 10 2023

Crossrefs

Cf. A034886, A352547, A360182.

Sequence in context: A153768 A371106 A371054 * A092194 A134307 A279775

Adjacent sequences: A360178 A360179 A360180 * A360182 A360183 A360184

Keyword

nonn,base,more,less

Author

Zhining Yang, Jan 28 2023

Status

approved