cp's OEIS Frontend

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.

A300669 Positive numbers k with two consecutive ones in the binary representation of 1/k.

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%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