Lunation number increases at full moon, not new moon?

[dannylin108]

Here's date vs lunation number. Why it increases at full moon?

2023-02-04: 1238
2023-02-05: 1238
2023-02-06: 1239
2023-02-07: 1239

Also, why is BLN used, it got obsolete in 1983, as wikipedia says

[jasonsturges]

Brown lunation was requested.

There are many lunation numbers, I might consider an option to specify different lunation strategy.