I noticed this a few days ago, but given the holidays I haven't spent time on it.

Generate the e's for a number, example 259. The odd e's for that 259 appear as a[t] in (e, 1) are:

[517, 509, 493, 469, 437, 397, 349, 293, 229, 157, 77]

I decided to play with them for no specific reason, but I mapped the numbers through a getU function and I got the following:

[258, 254, 246, 234, 218, 198, 174, 146, 114, 78, 38]

What stands out is 146 and 114 (and 78). The Big N for 259 is 114 and the Big Shadow N is 146. I didn't expect this, but I checked with a few other numbers and it seems to hold for those as well. Another thing, 78 is also a value in (3, 259) but belongs to a different chain. Anyone looked into this before? Anyone knows why this seems to occur?