A336231 Integers whose binary digit expansion has an even number of 0’s between any two consecutive 1’s.

0, 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 15, 16, 18, 19, 24, 25, 28, 30, 31, 32, 33, 36, 38, 39, 48, 50, 51, 56, 57, 60, 62, 63, 64, 66, 67, 72, 73, 76, 78, 79, 96, 97, 100, 102, 103, 112, 114, 115, 120, 121, 124, 126, 127, 128, 129, 132, 134, 135, 144, 146, 147, 152

Offset

1,3

Comments

If m is a term then 2*m is a term too.

If m is an odd term and k is odd then 2^k*m+1 is a term. - Robert Israel, Jul 16 2020

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Daniel Glasscock, Joel Moreira, and Florian K. Richter, Additive transversality of fractal sets in the reals and the integers, arXiv:2007.05480 [math.NT], 2020. See Aeven p. 34.

Example

9 is 1001 in binary, with 2 (an even number) consecutive zeroes, so 9 is a term.

Maple

B[1]:= {1}: S[0]:= {0}: S[1]:= {1}: count:= 2:
for d from 2 while count < 200 do
  B[d]:= map(op, {seq(map(t -> t*2^k+1, B[d-k]), k=1..d-1, 2)});
  S[d]:= B[d] union map(`*`, S[d-1], 2);
  count:= count+nops(S[d]);
od:
[seq(op(sort(convert(S[t], list))), t=0..d-1)]; # Robert Israel, Jul 16 2020

Prog

(PARI) isok(n) = {my(vpos = select(x->(x==1), binary(n), 1)); for (i=1, #vpos-1, if ((vpos[i+1]-vpos[i]-1) % 2, return (0)); ); return(1); }

Crossrefs

Cf. A007088, A060142, A336232.

Sequence in context: A023759 A004742 A277817 * A100290 A344341 A140181

Adjacent sequences: A336228 A336229 A336230 * A336232 A336233 A336234

Keyword

nonn,base

Author

Michel Marcus, Jul 13 2020

Status

approved