A300889 -id:A300889 - cp's OEIS frontend

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

Offset: 0

Rémy Sigrist, Mar 14 2018

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.

			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

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)))

Cf. A003714, A070939, A195156, A300889.

a(n) = forstep (k=1, oo, 2, if (bitand(k*n, 2*k*n)==0, return (k)))

a(n) = A300889(n) / n for any n > 0.
a(2*n) = a(n).
a(n) = 1 iff n belongs to A003714.

A377413 a(n) is the least term of A126684 of the form k*n with k > 0.

Original entry on oeis.org

0, 1, 2, 21, 4, 5, 42, 21, 8, 81, 10, 341, 84, 65, 42, 1365, 16, 17, 162, 1045, 20, 21, 682, 69, 168, 325, 130, 81, 84, 261, 2730, 341, 32, 1089, 34, 1365, 324, 4181, 2090, 273, 40, 1025, 42, 5461, 1364, 5445, 138, 20821, 336, 1029, 650, 4437, 260, 5141, 162

Offset: 0

Rémy Sigrist, Oct 27 2024

			The first terms, in decimal and in binary, are:
  n   a(n)  bin(a(n))
  --  ----  ---------
   0     0          0
   1     1          1
   2     2         10
   3    21      10101
   4     4        100
   5     5        101
   6    42     101010
   7    21      10101
   8     8       1000
   9    81    1010001
  10    10       1010
  11   341  101010101
  12    84    1010100

Rémy Sigrist, Table of n, a(n) for n = 0..10000
Rémy Sigrist, C++ program

See A300889 for a similar sequence.

Cf. A126684, A377412.

a(n) = A377412(n)*n.
a(n) >= A300889(n) for any n > 0.
a(n) = n iff n belongs to A126684.

cp's OEIS Frontend

A300867 a(n) is the least positive k such that k * n is a Fibbinary number (A003714).

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