Differences — successive differences

Accumulate — cumulative sums

Union — unique elements in a single list or between lists

Tally — tally distinct elements, listing them with their multiplicities

BinCounts, BinLists — count, list elements in a sequence of bins

Cases — list elements matching a pattern

Count — count elements matching a pattern

Position — positions of elements

list/.rule — replace elements according to a rule

ArrayRules — convert to positionvalue sparse array form

FromDigits — convert to numbers, polynomials, etc.

ToString — convert to a string

FindSequenceFunction — find functional forms for integer sequences