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.

Original entry on oeis.org

5, 9, 10, 11, 13, 17, 18, 19, 20, 21, 22, 23, 25, 26, 27, 29, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 49, 50, 52, 53, 54, 55, 57, 58, 59, 61, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89
Offset: 1

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Author

Rémy Sigrist, Mar 11 2018

Keywords

Comments

Equivalently, these are the numbers k such that A300655(k) > 1.
Equivalently, these are the numbers k such that A300653(k, 3) = 3.
If n belongs to this sequence then 2*n belongs to this sequence.
This sequence has similarities with A004780; here 1/k has two consecutive ones in binary, there k has two consecutive ones in binary.
See A300630 for the complementary sequence.

Examples

			The first terms, alongside the binary representation of 1/a(n), are:
  n    a(n)    bin(1/a(n)) with repeating digits in parentheses
  --   ----    ------------------------------------------------
   1      5    0.(0011)
   2      9    0.(0001110)
   3     10    0.0(0011)
   4     11    0.(0001011101)
   5     13    0.0(00100111011)
   6     17    0.(00001111)
   7     18    0.0(000111)
   8     19    0.(000011010111100101)
   9     20    0.00(0011)
  10     21    0.(000011)
		

Crossrefs

Cf. A004780, A300653, A300655, A300630 (complement).

Programs

  • 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)