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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 December 12 20:12 EST 2019. Contains 329961 sequences. (Running on oeis4.)