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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.

%I A333369 #33 Aug 04 2022 16:30:35
%S A333369 1,3,5,7,9,13,15,17,19,22,31,35,37,39,44,51,53,57,59,66,71,73,75,79,
%T A333369 88,91,93,95,97,100,111,122,135,137,139,144,153,157,159,166,173,175,
%U A333369 179,188,193,195,197,212,221,223,225,227,229,232,252,272,292,300,315,317,319,322
%N 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.
%C A333369 Inspired by the 520th problem of Project Euler (see link) where such a number is called a "simber".
%C A333369 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
%C A333369 The number of terms with respectively 1, 2, 3, ... digits is 5, 24, 130, ...
%H A333369 Michel Marcus, <a href="/A333369/b333369.txt">Table of n, a(n) for n = 1..10000</a>
%H A333369 Project Euler, <a href="https://projecteuler.net/problem=520">Problem 520: Simbers</a>.
%e A333369 656 is a 3-digit term because it has one 5 and two 6's.
%e A333369 447977 is a 6-digit term because it has one 9, two 4's and three 7's.
%t A333369 seqQ[n_] := AllTrue[Tally @ IntegerDigits[n], EvenQ[Plus @@ #] &]; Select[Range[300], seqQ] (* _Amiram Eldar_, Mar 17 2020 *)
%o A333369 (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
%o A333369 (Python)
%o A333369 def ok(n): s = str(n); return all(s.count(d)%2 == int(d)%2 for d in set(s))
%o A333369 print([k for k in range(323) if ok(k)]) # _Michael S. Branicky_, Apr 15 2022
%Y A333369 Cf. A108571 (finite subsequence), A353007.
%K A333369 nonn,base
%O A333369 1,2
%A A333369 _Bernard Schott_, Mar 17 2020