A269003 Numbers having the same parity of numbers of 1's in bases 2 and -2.

0, 1, 4, 5, 10, 11, 16, 17, 20, 21, 26, 27, 34, 35, 38, 39, 40, 41, 44, 45, 46, 47, 50, 51, 58, 59, 64, 65, 68, 69, 74, 75, 80, 81, 84, 85, 90, 91, 98, 99, 102, 103, 104, 105, 108, 109, 110, 111, 114, 115, 122, 123, 130, 131, 134, 135, 136, 137, 140, 141, 142

Offset

0,3

Comments

Or the numbers n for which the number of 1's in A039724(n) and the number of 1's in the binary expansion of n have the same parity.

The sequence contains the Moser-de Bruijn numbers (A000695) as a subsequence.

The first differences are: 1, 3, 1, 5, 1, 5, 1, 3, 1, 5, 1, 7, 1, 3, 1, 1, 1, 3, 1, 1, 1, 3, 1, 7, 1, 5, 1, 3, 1, 5, 1, 5, 1, 3, 1, 5, 1, 7, 1, 3, 1, 1, 1, 3, 1, 1, 1, 3, 1, 7, 1, 7, 1, 3, 1, 1, 1, 3, 1, 1, 1, 3, 1, 3, 1, 1, 1, 3, 1, 1, 1, 1, 1, 3, 1, 5, 1, 5, 1, 3, 1, 1, 1, 1, 1, 3, 1, ...

Is this sequence unbounded?

Links

Table of n, a(n) for n=0..60.

Vladimir Shevelev, Two analogs of Thue-Morse sequence, arXiv:1603.04434 [math.NT], 2016.

Eric Weisstein's World of Mathematics, Moser-de Bruijn Sequence

Eric Weisstein's World of Mathematics, Negabinary

Crossrefs

Cf. A010060, A039724, A000695, A268865, A268866.

Sequence in context: A102856 A285135 A037353 * A246390 A047257 A327311

Adjacent sequences: A269000 A269001 A269002 * A269004 A269005 A269006

Keyword

nonn,base

Author

Vladimir Shevelev, Feb 17 2016

Extensions

More terms from Peter J. C. Moses, Feb 17 2016

Status

approved