# Preparing odd integers using quantum computation

This is just a basic question. I need to output odd integers till $$15$$, i.e $$1,3,5,7,9,11,13,15$$. Since $$15$$ requires $$4$$ bits, I prepare initial state by using Hadamard gate on initial $$|0\rangle$$, i.e $$H|0\rangle \otimes H|0\rangle \otimes H|0\rangle$$ $$=|000\rangle+|001\rangle+|010\rangle+|011\rangle+|100\rangle+|101\rangle+|110\rangle+|111\rangle.$$ Then take the tensor product with $$|1\rangle$$, i.e $$(H|0\rangle \otimes H|0\rangle \otimes H|0\rangle)|1\rangle$$ $$=|0001\rangle+|0011\rangle+|0101\rangle+|0111\rangle+|1001\rangle+|1011\rangle+|1101\rangle+|1111\rangle.$$ Is this right? Actually, I know the ideas but don't know how to write it in the quantum computing terms, that involves using terms as registers, qubits