A300867 - OEIS

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

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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,look,base

AUTHOR

Rémy Sigrist, Mar 14 2018

STATUS

approved