The quasi-nice stuff (numbers x where x and x^2 are pandigital) makes me pretty confident that there are in fact nice numbers at triple-digit bases, since the current heuristics accurately model their density (first medium, then super low, then super high)

@Conflux I think it's be pretty hard to find one though, so this market will most likely never resolve

@Conflux (see tinyurl.com/confluxblog/post/is-69-unique, tinyurl.com/confluxblog/post/progress-update-on-the-search-for-nice-numbers)

@Conflux Yeah, I think they are a pretty strong argument that they exist and we just need to look to higher bases. Only problem is that it will take a very long time to do so if there are no new insights.

@Conflux By the way, what is the highest base that has been fully checked for nice numbers (as far as you know) to date?

@JosephNoonan 48. Highest search I know of is nicenumbers.net (c/o @wasabipesto)

@Conflux I see, so everything up to 44 has been searched for not only nice numbers but also near misses and quasi-nice numbers, while everything up to 48 has been searched for nice numbers, but not necessarily those other types?

@JosephNoonan I think so! Wasabipesto used to have a blogpost on that site describing their process, but I can't find it anymore

@JosephNoonan That's correct! Through base 44 we have information on the niceness distribution and near misses for the entire base range. Through base 48 we checked for nice numbers only. I don't save any information on quasi-nice numbers.

@Conflux @wasabipesto You may also be interested to know that I'm now searching for some new nice number variants: