A333369 Positive integers 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.

1, 3, 5, 7, 9, 13, 15, 17, 19, 22, 31, 35, 37, 39, 44, 51, 53, 57, 59, 66, 71, 73, 75, 79, 88, 91, 93, 95, 97, 100, 111, 122, 135, 137, 139, 144, 153, 157, 159, 166, 173, 175, 179, 188, 193, 195, 197, 212, 221, 223, 225, 227, 229, 232, 252, 272, 292, 300, 315, 317, 319, 322

Offset: 1

Author

Bernard Schott, Mar 17 2020

Keywords

• nonn
• base

Comments

Inspired by the 520th problem of Project Euler (see link) where such a number is called a "simber".

This sequence has little mathematical interest. The name "simber", which might be interpreted as "silly number", is deprecated. - N. J. A. Sloane, Aug 04 2022

The number of terms with respectively 1, 2, 3, ... digits is 5, 24, 130, ...

Examples

			656 is a 3-digit term because it has one 5 and two 6's.
447977 is a 6-digit term because it has one 9, two 4's and three 7's.
		

Links

• Michel Marcus, Table of n, a(n) for n = 1..10000
• Project Euler, Problem 520: Simbers.

Crossrefs

Cf. A108571 (finite subsequence), A353007.

Programs

Mathematica

seqQ[n_] := AllTrue[Tally @ IntegerDigits[n], EvenQ[Plus @@ #] &]; Select[Range[300], seqQ] (* Amiram Eldar, Mar 17 2020 *)

PARI

isok(m) = my(d=digits(m), s=Set(d)); for (i=1, #s, if (#select(x->(x==s[i]), d) % 2 != (s[i] % 2), return (0))); return (1); \\ Michel Marcus, Mar 17 2020

Python

def ok(n): s = str(n); return all(s.count(d)%2 == int(d)%2 for d in set(s))
print([k for k in range(323) if ok(k)]) # Michael S. Branicky, Apr 15 2022