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

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

1,1

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.

Links

Table of n, a(n) for n=1..66.

Example

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)

Prog

(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)

Crossrefs

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

Sequence in context: A187713 A101082 A277706 * A166934 A257739 A094695

Adjacent sequences: A300666 A300667 A300668 * A300670 A300671 A300672

Keyword

nonn,base

Author

Rémy Sigrist, Mar 11 2018

Status

approved