The Moser-de Bruijn sequence is the increasing sequence of nonnegative integers that are sums of distinct nonnegative integer powers of 4, including the empty sum 0. The first few are 0, 1, 4, 5, 16, 17, 20, 21, 64, 65, 68, 69, 80, 81, 84, ... (OEIS A000695). These numbers also satisfy the interesting properties that their binary digit sum equals their quaternary digit sum, and that they have identical representations in binary and negabinary.
Moser-de Bruijn Sequence
See also
Binary, Negabinary, QuaternaryExplore with Wolfram|Alpha
References
Allouche, J.-P. and Shallit, J. "The Ring of
-Regular Sequences." Theor. Comput. Sci. 98,
163-197, 1992.de Bruijn, N. G. "Some Direct Decompositions
of the Set of Integers." Math. Comput. 18, 537-546, 1964.Moser,
L. "An Application of Generating Series." Math. Mag. 35,
37-38, 1962.Sloane, N. J. A. Sequence A000695/M3259
in "The On-Line Encyclopedia of Integer Sequences."Referenced on Wolfram|Alpha
Moser-de Bruijn SequenceCite this as:
Weisstein, Eric W. "Moser-de Bruijn Sequence." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Moser-deBruijnSequence.html