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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 A348221 A132429 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 21 07:33 EDT 2024. Contains 373540 sequences. (Running on oeis4.)