PostgreSQL B-tree, good monotonic values?
With B-Tree indexes, more importantly is the cardinality of the data you're indexing. The more unique the data is in the index, generally the better candidate it is for a B-Tree index because it'll result in a much more full tree with many branches and leaves. A very non-unique field, like a boolean based field, will always only have two distinct values, and therefore is very repetitive resulting in two short but wide branches and doesn't filter down the data as much as a more unique field.
Since you're planning to index a BIGINT field with randomized values, it should lead to very unique data and the B-Tree index should perform very well, regardless of the monotonicness of those values. Additionally, if you're only inserting 30 values a month, your table must be tiny so you should have no worries at all regarding using a B-Tree index. B-Tree indexes handle billions of rows just fine.
To answer your actual question, yes monotonic values in a B-Tree index reduce fragmentation initially and therefor are more efficient, but again this is probably a minimal concern based on the fact that your values will be very unique and your overall amount of data being tiny.