A338744 When a(n) is even, a(n) is the number of odd digits present so far in the sequence, a(n) included.

0, 1, 3, 2, 5, 7, 4, 9, 11, 13, 10, 15, 17, 19, 21, 18, 23, 25, 20, 27, 29, 22, 31, 24, 33, 26, 35, 28, 37, 39, 41, 34, 43, 36, 45, 38, 47, 49, 40, 51, 42, 53, 44, 55, 46, 57, 48, 59, 61, 52, 63, 54, 65, 56, 67, 58, 69, 71, 73, 75, 77, 79, 70, 81, 72, 83, 74, 85, 76, 87, 78, 89, 91, 93, 95, 97, 99, 90, 101

Offset: 1

Author

Eric Angelini and Carole Dubois, Nov 06 2020

Keywords

• base
• nonn

Comments

The odd nonnegative integers are present in their natural order. Some even natural integers will never appear (6 for instance).

Examples

			The first even term is a(1) = 0 and there is indeed 0 odd digit so far in the sequence;
The next even term is a(4) = 2 and there are now 2 odd digits so far (1 and 3);
The next even term is a(7) = 4 and there are now 4 odd digits so far (1, 3, 5 and 7);
...
The even term a(11) = 10 and there are indeed 10 odd digits in the sequence so far (1, 3, 5, 7, 9, 1, 1, 1, 3 and 1); etc.
		

Crossrefs

Cf. A338741, A338742, A338743, A338745, A338746 (variants on the same idea), A196564.

Programs

Mathematica

Block[{a = {0}, c = 0}, Do[Block[{k = 1, s}, While[If[EvenQ[k], Nand[FreeQ[a, k], k == c + Set[s, Total@ DigitCount[k, 10, {1, 3, 5, 7, 9}]]], ! FreeQ[a, k]], k++]; If[EvenQ[k], c += s, c += Total@ DigitCount[k, 10, {1, 3, 5, 7, 9}]]; AppendTo[a, k]], {i, 78}]; a] (* Michael De Vlieger, Nov 06 2020 *)