A338741 When a(n) is odd, a(n) is the number of odd digits present so far in the sequence, a(n) included.

0, 1, 2, 4, 6, 8, 10, 3, 12, 5, 14, 7, 16, 9, 11, 13, 15, 17, 18, 20, 22, 24, 26, 28, 30, 32, 21, 34, 23, 36, 25, 38, 27, 40, 42, 44, 46, 48, 50, 29, 31, 33, 35, 37, 39, 52, 41, 54, 43, 56, 45, 58, 47, 60, 62, 64, 66, 68, 70, 49, 51, 53, 55, 57, 59, 72, 61, 74, 63, 76, 65, 78, 67, 80, 82, 84, 86, 88, 90, 69

Offset: 1

Author

Eric Angelini and Carole Dubois, Nov 06 2020

Keywords

• base
• nonn

Comments

The even nonnegative integers are present in their natural order. Some odd natural integers will never appear (19 for instance).

Examples

			The first odd term is a(2) = 1 and there is indeed 1 odd digit so far in the sequence (1 itself);
The next odd term is a(8) = 3 and there are now 3 odd digits so far (1, 1 and 3);
The next odd term is a(10) = 5 and there are now 5 odd digits so far (1, 1, 3, 1 and 5);
...
The next odd term is a(18) = 17 and there are indeed 17 odd digits so far in the sequence (1, 1, 3, 1, 5, 1, 7, 1, 9, 1, 1, 1, 3, 1, 5, 1, 7); etc.
		

Crossrefs

Cf. A338742, A338743, A338744, A338745, A338746 (variants on the same idea), A196564.

Programs

Mathematica

Block[{a = {0}, c = 0}, Do[Block[{k = 1, s}, While[If[OddQ[k], Nand[FreeQ[a, k], k == c + Set[s, Total@ DigitCount[k, 10, {1, 3, 5, 7, 9}]]], ! FreeQ[a, k]], k++]; If[OddQ[k], c += s, c += Total@ DigitCount[k, 10, {1, 3, 5, 7, 9}]]; AppendTo[a, k]], {i, 79}]; a] (* Michael De Vlieger, Nov 06 2020 *)