A283870 For all n, the set consisting of the terms {a(1), a(2), a(3), ..., a(n)} has an odd number or 0 of digits 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9.

1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 22, 33, 44, 55, 66, 77, 88, 99, 101, 1001, 1010, 1100, 1111, 1122, 1133, 1144, 1155, 1166, 1177, 1188, 1199, 1212, 1221, 1313, 1331, 1414, 1441, 1515, 1551, 1616, 1661, 1717, 1771, 1818, 1881, 1919, 1991, 2002, 2020, 2112, 2121, 2200, 2211, 2222, 2233, 2244, 2255, 2266, 2277, 2288

Offset

1,2

Comments

The sequence is started with a(1) = 1 and always extended with the smallest integer not yet present and not leading to a contradiction.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Formula

a(n) = A283871(n-10) for n >= 20. - Robert Israel, Jan 07 2024

Example

The set consisting of the first 20 terms is {1,2,3,4,5,6,7,8,9,11,22,33,44,55,66,77,88,99,101,1001}; we count three 0's, seven 1's, three 2's, three 3's, three 4's, etc. All those quantities of digits are odd numbers.

Maple

filter:= proc(n) local L; L:= convert(n, base, 10);
   andmap(t -> numboccur(t, L)::even, L) end proc:
1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 22, 33, 44, 55, 66, 77, 88, 99, 101, op(select(filter, [$1000..9999])); # Robert Israel, Jan 07 2024

Crossrefs

Cf. A283871.

Sequence in context: A109882 A109872 A030285 * A175688 A048321 A071267

Adjacent sequences: A283867 A283868 A283869 * A283871 A283872 A283873

Keyword

nonn,base

Author

Eric Angelini and Jean-Marc Falcoz, Mar 17 2017

Extensions

Definition corrected by Robert Israel, Jan 07 2024

Status

approved