IntegerSequences: a package for computing with k-regular sequences. IntegerSequences is a Mathematica package for computing with integer sequences. Its support for k-regular sequences includes basic closure properties, guessing recurrences, and computing automata. Recent applications have included establishing the structure of extremal a/b-power-free words, obtaining a product formula for the generating function enumerating binomial coefficients by their p-adic valuations, and proving congruences for combinatorial sequences modulo prime powers.

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