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

1,1

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

Cf. A333369, A353007, A353736.

Sequence in context: A278679 A000349 A327118 * A036919 A020067 A066118

Adjacent sequences: A353732 A353733 A353734 * A353736 A353737 A353738

Keyword

nonn,base

Author

Michael S. Branicky, May 06 2022

Status

approved