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Tuples

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A tuple is an ordered list of elements.[1] That is, it is a finite sequence.

There are various ways to encode in a nonnegative integer a tuple of nonnegative-integers or natural numbers of an arbitrary, but finite length. These include the binary run-length encoding or using exponent-tuple of the prime factorization. To encode specific -tuples (i.e. of the fixed length) see Marc LeBrun's method explained in A000695.

To encode a tuple of integers (including zero and negative numbers) of an arbitrary, but finite length, one can use the factorization of a positive rational number to its integer prime factors, and then use one of the orderings of rational numbers like Stern-Brocot tree to map them to nonnegative integers.

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