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
Examples
9 is 1001 in binary, with 2 (an even number) consecutive zeros, so 9 is a term.
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.
Programs
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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 -
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);}
Comments