

A336232


Integers whose binary digit expansion has a prime number of 0’s between any two consecutive 1’s.


2



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
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OFFSET

1,3


COMMENTS

If m is a term then 2*m is a term too.
If m is an odd term and p is prime then 2^(p+1)*m+1 is a term.  Robert Israel, Jul 15 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 Aprime p. 34.
Benjamin Matson and Elizabeth Sattler, Slimited shifts, arXiv:1708.08511 [math.DS], 2017. See page 2.


EXAMPLE

9 is 1001 in binary, with 2 (a prime) 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^(p+1)+1, B[dp1]), p=select(isprime, [$2..d2]))});
S[d]:= B[d] union map(`*`, S[d1], 2);
count:= count+nops(S[d]);
od:
[seq(op(sort(convert(S[t], list))), t=0..d1)]; # Robert Israel, Jul 16 2020


PROG

(PARI) isok(n) = {my(vpos = select(x>(x==1), binary(n), 1)); for (i=1, #vpos1, if (!isprime(vpos[i+1]vpos[i]1), return (0)); ); return(1); }


CROSSREFS

Cf. A007088, A336231.
Sequence in context: A036349 A155562 A048715 * A242662 A335851 A028982
Adjacent sequences: A336229 A336230 A336231 * A336233 A336234 A336235


KEYWORD

nonn,base,look


AUTHOR

Michel Marcus, Jul 13 2020


STATUS

approved



