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 A300669 #4 Mar 11 2018 17:17:21 %S A300669 5,9,10,11,13,17,18,19,20,21,22,23,25,26,27,29,33,34,35,36,37,38,39, %T A300669 40,41,42,43,44,45,46,47,49,50,52,53,54,55,57,58,59,61,65,66,67,68,69, %U A300669 70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89 %N A300669 Positive numbers k with two consecutive ones in the binary representation of 1/k. %C A300669 Equivalently, these are the numbers k such that A300655(k) > 1. %C A300669 Equivalently, these are the numbers k such that A300653(k, 3) = 3. %C A300669 If n belongs to this sequence then 2*n belongs to this sequence. %C A300669 This sequence has similarities with A004780; here 1/k has two consecutive ones in binary, there k has two consecutive ones in binary. %C A300669 See A300630 for the complementary sequence. %e A300669 The first terms, alongside the binary representation of 1/a(n), are: %e A300669 n a(n) bin(1/a(n)) with repeating digits in parentheses %e A300669 -- ---- ------------------------------------------------ %e A300669 1 5 0.(0011) %e A300669 2 9 0.(0001110) %e A300669 3 10 0.0(0011) %e A300669 4 11 0.(0001011101) %e A300669 5 13 0.0(00100111011) %e A300669 6 17 0.(00001111) %e A300669 7 18 0.0(000111) %e A300669 8 19 0.(000011010111100101) %e A300669 9 20 0.00(0011) %e A300669 10 21 0.(000011) %o A300669 (PARI) is(n) = my (f=1/max(2, n), s=Set()); while (!setsearch(s, f), if (floor(f*4)==3, return (1), s=setunion(s, Set(f)); f=frac(f*2))); return (0) %Y A300669 Cf. A004780, A300653, A300655, A300630 (complement). %K A300669 nonn,base %O A300669 1,1 %A A300669 _Rémy Sigrist_, Mar 11 2018