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The sequence of Hamming numbers 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 27, 30, 32, 36, … (A051037) consists of all numbers of the form 2

^{i}·3^{j}·5^{k}where*i*,*j*and*k*are non-negative integers. Edsger Dijkstra introduced this sequence to computer science in his book*A Discipline of Programming*, and it has been a staple of beginning programming courses ever since. Dijkstra wrote a program based on three axioms:Axiom 1: The value 1 is in the sequence.

Axiom 2: If

Axiom 3: The sequence contains no other values other than those that belong to it on account of Axioms 1 and 2.

Axiom 2: If

*x*is in the sequence, so are 2 **x*, 3 **x*, and 5 **x*.Axiom 3: The sequence contains no other values other than those that belong to it on account of Axioms 1 and 2.

Your task is to write a program to compute the first thousand terms of the Hamming sequence.

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