A338742 When a(n) is even, a(n) is the number of even digits present so far in the sequence, a(n) included.

1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 2, 23, 4, 25, 6, 27, 8, 29, 10, 31, 33, 35, 37, 39, 41, 12, 43, 14, 45, 16, 47, 18, 20, 22, 24, 26, 28, 49, 30, 51, 53, 55, 57, 59, 61, 32, 63, 34, 65, 36, 67, 38, 40, 42, 44, 46, 48, 69, 50, 71, 73, 75, 77, 79, 81, 52, 83, 54, 85, 56, 87, 58, 60, 62, 64, 66, 68, 89

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.

Examples

			The first even term is a(12) = 2 and there are indeed 2 even digits so far in the sequence (the 2 from 21 and 2 itself);
The next even term is a(14) = 4 and there are now 4 even digits so far (2, 2, 2 and 4);
The next even term is a(16) = 6 and there are now 6 even digits so far (2, 2, 2, 4, 2 and 6); etc.
		

Crossrefs

Cf. A338741, A338743, A338744, A338745, A338746 (variants on the same idea), A196563.

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, {0, 2, 4, 6, 8}]]], ! FreeQ[a, k]], k++]; If[EvenQ[k], c += s, c += Total@ DigitCount[k, 10, {0, 2, 4, 6, 8}]]; AppendTo[a, k]], {i, 79}]; a] (* Michael De Vlieger, Nov 06 2020 *)