A300867 a(n) is the least positive k such that k * n is a Fibbinary number (A003714).

1, 1, 1, 3, 1, 1, 3, 3, 1, 1, 1, 3, 3, 5, 3, 11, 1, 1, 1, 7, 1, 1, 3, 3, 3, 13, 5, 3, 3, 5, 11, 11, 1, 1, 1, 39, 1, 1, 7, 7, 1, 1, 1, 3, 3, 13, 3, 7, 3, 21, 13, 23, 5, 5, 3, 3, 3, 9, 5, 11, 11, 9, 11, 43, 1, 1, 1, 35, 1, 1, 39, 15, 1, 1, 1, 31, 7, 57, 7, 7, 1

Offset

0,4

Comments

This sequence is well defined: for any positive n, according to the pigeonhole principle, A195156(i) mod n = A195156(j) mod n for some distinct i and j, hence n divides f = abs(A195156(i) - A195156(j)), and as f is a Fibbinary number, a(n) <= f/n.

All terms are odd.

Links

Rémy Sigrist, Table of n, a(n) for n = 0..10000

Rémy Sigrist, Colored logarithmic scatterplot of the first 1000000 terms (where the color is function of A070939(n * a(n)))

Formula

a(n) = A300889(n) / n for any n > 0.

a(2*n) = a(n).

a(n) = 1 iff n belongs to A003714.

Example

The first terms, alongside the binary representation of n * a(n), are:
  n  a(n)   bin(n * a(n))
  -- ----   -------------
   0    1           0
   1    1           1
   2    1          10
   3    3        1001
   4    1         100
   5    1         101
   6    3       10010
   7    3       10101
   8    1        1000
   9    1        1001
  10    1        1010
  11    3      100001
  12    3      100100
  13    5     1000001
  14    3      101010
  15   11    10100101
  16    1       10000
  17    1       10001
  18    1       10010
  19    7    10000101
  20    1       10100

Prog

(PARI) a(n) = forstep (k=1, oo, 2, if (bitand(k*n, 2*k*n)==0, return (k)))

Crossrefs

Cf. A003714, A070939, A195156, A300889.

Sequence in context: A307501 A169941 A099545 * A269301 A348221 A132429

Adjacent sequences: A300864 A300865 A300866 * A300868 A300869 A300870

Keyword

nonn,base

Author

Rémy Sigrist, Mar 14 2018

Status

approved