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A300867 a(n) is the least positive k such that k * n is a Fibbinary number (A003714). 2
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 (list; graph; refs; listen; history; text; internal format)
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 A132429 A046540

Adjacent sequences:  A300864 A300865 A300866 * A300868 A300869 A300870

KEYWORD

nonn,base

AUTHOR

Rémy Sigrist, Mar 14 2018

STATUS

approved

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Last modified June 20 21:23 EDT 2021. Contains 345247 sequences. (Running on oeis4.)