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%I #12 Mar 15 2018 06:18:20
%S 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,
%T 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,
%U 11,43,1,1,1,35,1,1,39,15,1,1,1,31,7,57,7,7,1
%N a(n) is the least positive k such that k * n is a Fibbinary number (A003714).
%C 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.
%C All terms are odd.
%H Rémy Sigrist, <a href="/A300867/b300867.txt">Table of n, a(n) for n = 0..10000</a>
%H Rémy Sigrist, <a href="/A300867/a300867.png">Colored logarithmic scatterplot of the first 1000000 terms</a> (where the color is function of A070939(n * a(n)))
%F a(n) = A300889(n) / n for any n > 0.
%F a(2*n) = a(n).
%F a(n) = 1 iff n belongs to A003714.
%e The first terms, alongside the binary representation of n * a(n), are:
%e n a(n) bin(n * a(n))
%e -- ---- -------------
%e 0 1 0
%e 1 1 1
%e 2 1 10
%e 3 3 1001
%e 4 1 100
%e 5 1 101
%e 6 3 10010
%e 7 3 10101
%e 8 1 1000
%e 9 1 1001
%e 10 1 1010
%e 11 3 100001
%e 12 3 100100
%e 13 5 1000001
%e 14 3 101010
%e 15 11 10100101
%e 16 1 10000
%e 17 1 10001
%e 18 1 10010
%e 19 7 10000101
%e 20 1 10100
%o (PARI) a(n) = forstep (k=1, oo, 2, if (bitand(k*n, 2*k*n)==0, return (k)))
%Y Cf. A003714, A070939, A195156, A300889.
%K nonn,base
%O 0,4
%A _Rémy Sigrist_, Mar 14 2018
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