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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, 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
Sequence in context: A307501 A169941 A099545 * A269301 A348221 A132429
KEYWORD
nonn,base
AUTHOR
Rémy Sigrist, Mar 14 2018
STATUS
approved

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Last modified June 21 07:33 EDT 2024. Contains 373540 sequences. (Running on oeis4.)