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

Author

Eric Angelini and Jean-Marc Falcoz, Mar 17 2017

Keywords

• nonn
• base

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.

Examples

			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.
		

Links

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

Crossrefs

Cf. A283871.

Programs

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

Formula

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

Extensions

Definition corrected by Robert Israel, Jan 07 2024