**If A = {a_1, a_2, a_3...} is the Moser-de Bruijn sequence A000695 (consisting of sums of distinct powers of 4) and A' = {2a_1, 2a_2, 2a_3...} then this sequence, let's call it B, is the union of A and A'. Its significance, alluded to in the entry for the Moser-de Bruijn sequence, is that its sumset, B+B, = {b_i + b_j : i, j natural numbers} consists of the nonnegative integers; and it is the fastest-growing sequence with this property. It can also be described as a "basis of order two for the nonnegative integers".**

*0, 1, 2, 4, 5, 8, 10, 16, 17, 20, 21, 32, 34, 40, 42, 64, 65, 68, 69, 80, 81, 84, 85, 128*

*4 seqfan posts*

Index of A-numbers in seqfan: by ascending order by month by frequency by keyword

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