A107909 Numbers having no consecutive zeros or no consecutive ones in binary representation.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 18, 20, 21, 22, 23, 26, 27, 29, 30, 31, 32, 33, 34, 36, 37, 40, 41, 42, 43, 45, 46, 47, 53, 54, 55, 58, 59, 61, 62, 63, 64, 65, 66, 68, 69, 72, 73, 74, 80, 81, 82, 84, 85, 86, 87, 90, 91, 93, 94, 95, 106, 107, 109, 110, 111

Offset: 0

Author

Reinhard Zumkeller, May 28 2005

Keywords

• nonn
• base
• easy

Comments

Union of A003754 and A003714, complement of A107911;

a(A023548(n+2)) = A052940(n+1) for n>0;

a(A001924(n)) = A000225(n) = 2^n - 1;

a(A000126(n)) = A000079(n) = 2^n for n>0;

A107910(n) = a(n+1) - a(n).

Links

• Ivan Neretin, Table of n, a(n) for n = 0..10000
• J. M. Dusel, Balanced parabolic quotients and branching rules for Demazure crystals, 2014.
• Index entries for 2-automatic sequences.

Crossrefs

Cf. A007088, A107907.

Programs

Perl

foreach $n(1..100){$_=sprintf("%b",$n); print "$n\n" if !m/11/||!m/00/}
# Ivan Neretin, May 01 2016