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A353735
Number of n-digit terms in A333369.
6
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
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