This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A300630 #13 Jun 28 2018 04:50:16 %S A300630 1,2,3,4,6,7,8,12,14,15,16,24,28,30,31,32,48,51,56,60,62,63,64,96,102, %T A300630 112,120,124,126,127,128,192,195,204,224,240,248,252,254,255,256,384, %U A300630 390,399,408,448,451,455,480,496,504,508,510,511,512,768,771,775 %N A300630 Positive numbers k without two consecutive ones in the binary representation of 1/k. %C A300630 Equivalently, these are the numbers k such that A300655(k) = 1. %C A300630 Equivalently, these are the numbers k such that A300653(k, 3) > 3. %C A300630 If n belongs to this sequence then 2*n belongs to this sequence. %C A300630 This sequence has similarities with the Fibbinary numbers (A003714); here 1/k has no two consecutive ones in binary, there k has no two consecutive ones in binary. %C A300630 For any odd term k, there is at least one positive Fibbinary number, say f, such that k * f belongs to A000225. %C A300630 Apparently, the only Fibbinary numbers that belong to this sequence are the powers of 2 (A000079). %C A300630 See A300669 for the complementary sequence. %C A300630 Includes 2^k-1 for all k>=1. - _Robert Israel_, Jun 27 2018 %H A300630 Robert Israel, <a href="/A300630/b300630.txt">Table of n, a(n) for n = 1..629</a> %e A300630 The first terms, alongside the binary representation of 1/a(n), are: %e A300630 n a(n) bin(1/a(n)) with repeating digits in parentheses %e A300630 -- ---- ------------------------------------------------ %e A300630 1 1 1.(0) %e A300630 2 2 0.1(0) %e A300630 3 3 0.(01) %e A300630 4 4 0.01(0) %e A300630 5 6 0.0(01) %e A300630 6 7 0.(001) %e A300630 7 8 0.001(0) %e A300630 8 12 0.00(01) %e A300630 9 14 0.0(001) %e A300630 10 15 0.(0001) %e A300630 11 16 0.0001(0) %e A300630 12 24 0.000(01) %e A300630 13 28 0.00(001) %e A300630 14 30 0.0(0001) %e A300630 15 31 0.(00001) %e A300630 16 32 0.00001(0) %e A300630 17 48 0.0000(01) %e A300630 18 51 0.(00000101) %e A300630 19 56 0.000(001) %e A300630 20 60 0.00(0001) %p A300630 filter:= proc(n) local m,d,r; %p A300630 m:= n/2^padic:-ordp(n,2); %p A300630 d:= numtheory:-order(2,m); %p A300630 r:=(2^d-1)/m; %p A300630 Bits:-Or(r,2*r)=3*r %p A300630 end proc: %p A300630 select(filter, [$1..1000]); # _Robert Israel_, Jun 27 2018 %o A300630 (PARI) is(n) = my (f=1/max(2,n), s=Set()); while (!setsearch(s, f), if (floor(f*4)==3, return (0), s=setunion(s,Set(f)); f=frac(f*2))); return (1) %Y A300630 Cf. A000079, A000225, A003714, A300653, A300655, A300669. %K A300630 nonn,base %O A300630 1,2 %A A300630 _Rémy Sigrist_, Mar 10 2018