OFFSET
1,1
COMMENTS
Also the number of n-digit simbers, where a simber is a positive integer in which any odd digit, if present, occurs an odd number of times, and any even digit, if present, occurs an even number of times.
LINKS
Michael S. Branicky, Table of n, a(n) for n = 1..1002
Project Euler, Problem 520: Simbers.
FORMULA
From Bernard Schott, Jul 11 2022: (Start)
Conjecture 1: lim_{n->oo} a(2n+1)/a(2n-1) = 100.
Conjecture 2: lim_{n->oo} a(2n+2)/a(2n) = 81. (End)
EXAMPLE
There are five 1-digit terms in A333369: 1, 3, 5, 7, 9. Thus, a(1) = 5.
PROG
(Python)
def isA333369(n):
digits = list(map(int, str(n)))
return all(digits.count(d)%2 == d%2 for d in set(digits))
def a(n): return sum(1 for i in range(10**(n-1), 10**n) if isA333369(i))
print([a(n) for n in range(1, 7)]) # Michael S. Branicky, May 06 2022
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Michael S. Branicky, May 06 2022
STATUS
approved