Cumulative sum of odd digits

 

Hello Math-Fun,

I hope the definition below is clear, and the calculations correct.

But I have a lot of doubts.

Best,

É.

 

Definition

An even term T of the sequence S is the sum of all odd digits so far (including T’s digits).

We always try to extend S with the smallest even integer not leading to a contradiction.

Else we extend S with the smallest odd integer.

This is the lexicographically earliest sequence of distinct nonnegative integers with this property.

 

S = 0, 1, 3, 4, 5, 7, 9, 11, 30, 13, 15, 40, 17, 48, 19, 21, 23, 62,  

sum 0  1  4  4  9  16 25 27  30  34  40  40  48  48  58  59  62  62

 

S = 25, 74, 27, 29, 31, 33, 35, 110, 112, 114, 116, 118, 37, 132,

sum 67  74  81  90  94  100 108 110  112  114  116  118  128 132

 

S = 136, 39, 154, 41, 43, 45, 164, 172, 47, 180, 49, 51, 53, 55,

sum 136  148 154  155 158 163 164  172  179 180  189 195 203 213

 

S = 214, 57, 226, 59, 240, ...  

sum 214  226 226, 240 240

(not in the OEIS)

____________

[but soon...  thanks to Maximilian H. ! He was quick to correct my above (wrong) S]

Update:

> Hello Eric,

I (& my program) get already the 6th term different :

0, 1, 3, 4, 5, 10, 7, 18, 9, 30, 11, 13, 15, 42, 17, 19, 60, ...

As written on your web page, after the 5 the sum of odd digits is 9, so the "10" should be OK because including its odd digit 1, the sum is 10.

If my program is right, the sequence continues after the above ..., 60 :

... 21, 23, 64, 25, 76, 27, 92, 29, 102, 31, 33, 114, 116, 118, 35, 130, 134, 138, 37, 154, 39, 174, 41, 43, 45, 184, 194, 47, 49, 51, 53, 224, 55, 57, 246, 59, 260, 61, 63, 264, 65, 276, 67, 292, 69, 304, 71, 316, 73, 332, 338, 75, 358, 77, 79, 81, 83, 85, 87, 404, 89, 414, 91, 424, 93, 95, 97, 466, 99, 484, 101, 486, 103, 105, 107, 510, 516, 109, 534, 111, 542, 552, 113, ...

- Maximilian

(now submitted as https://oeis.org/draft/A357051)

(Ahem... my apologizes here, Maximilian – and thanks for your comment!-)

Two pix by Helmut Newton, seen here