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

1,2

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, ...

Links

Michel Marcus, Table of n, a(n) for n = 1..10000

Project Euler, Problem 520: Simbers.

Example

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.

Mathematica

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

Prog

(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

Crossrefs

Cf. A108571 (finite subsequence), A353007.

Sequence in context: A029740 A063425 A215806 * A064608 A024893 A337810

Adjacent sequences: A333366 A333367 A333368 * A333370 A333371 A333372

Keyword

nonn,base

Author

Bernard Schott, Mar 17 2020

Status

approved