A336232 Integers whose binary digit expansion has a prime number of 0’s between any two consecutive 1’s.
0, 1, 2, 4, 8, 9, 16, 17, 18, 32, 34, 36, 64, 65, 68, 72, 73, 128, 130, 136, 137, 144, 145, 146, 256, 257, 260, 272, 273, 274, 288, 290, 292, 512, 514, 520, 521, 544, 546, 548, 576, 577, 580, 584, 585, 1024, 1028, 1040, 1041, 1042, 1088, 1089, 1092, 1096, 1097
Offset: 1
Examples
9 is 1001 in binary, with 2 (a prime) consecutive zeroes, 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 Aprime p. 34.
- Benjamin Matson and Elizabeth Sattler, S-limited shifts, arXiv:1708.08511 [math.DS], 2017. See page 2.
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^(p+1)+1,B[d-p-1]),p=select(isprime,[$2..d-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 (!isprime(vpos[i+1]-vpos[i]-1), return (0));); return(1);}
Comments