A353735 Number of n-digit terms in A333369.

5, 24, 130, 792, 5080, 34584, 247360, 1817112, 13918720, 108848664, 869866240, 7169995032, 59085276160, 505735077144, 4311229112320, 37428004374552, 335520388710400, 2861870689152024, 27669446179225600, 223578655251963672, 2398913308953149440, 17708639883984065304

Offset: 1

Author

Michael S. Branicky, May 06 2022

Keywords

• nonn
• base

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.

Examples

			There are five 1-digit terms in A333369: 1, 3, 5, 7, 9. Thus, a(1) = 5.
		

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..1002
• Project Euler, Problem 520: Simbers.

Crossrefs

Cf. A333369, A353007, A353736.

Programs

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

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)