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A336231 Integers whose binary digit expansion has an even number of 0’s between any two consecutive 1’s. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified December 3 21:17 EST 2021. Contains 349468 sequences. (Running on oeis4.)