login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A300475 a(n) is the least positive k such that the binary representation n appears in front of the binary representation of 1/k (ignoring the radix point and the leading zeros and adding trailing zeros if necessary in case of a terminating expansion). 3
1, 1, 5, 1, 3, 5, 9, 1, 7, 3, 11, 5, 19, 9, 17, 1, 15, 7, 13, 25, 3, 23, 11, 21, 5, 19, 37, 9, 35, 17, 33, 1, 31, 15, 29, 7, 27, 53, 13, 25, 49, 3, 47, 23, 45, 11, 43, 21, 41, 81, 5, 39, 19, 75, 37, 9, 71, 35, 69, 17, 67, 33, 65, 1, 63, 31, 61, 15, 59, 29, 57 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

In other words, a(n) is the least k > 0 such that floor((2^i) / k) = n for some integer i >= 0.

This sequence is similar to A095156 for the base 2.

All terms are odd.

All terms appears infinitely many times (as a(n) equals at least a(2*n) or a(2*n + 1)).

See also A300428 for a similar sequence.

LINKS

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Rémy Sigrist, PARI program for A300475

Rémy Sigrist, Colored logarithmic scatterplot of the first 1000000 terms (where the color is function of A070939(n * a(n)))

FORMULA

a(2^k) = 1 for any k >= 0.

a(2^k - 1) = 2^k + 1 for any k > 1.

a(A000975(k)) = 3 for any k > 2.

a(A033138(k)) = 7 for any k > 4.

a(n) >= A300428(n).

EXAMPLE

The first terms, alongside the binary representation of 1/a(n) with the earliest occurrence of the binary representation of n in parentheses, are:

  n  a(n)    bin(1/a(n))

  -- ----    -----------

   1    1    (1).000...

   2    1    (1.0)000...

   3    5    0.00(11)001...

   4    1    (1.00)000...

   5    3    0.0(101)010...

   6    5    0.00(110)011...

   7    9    0.000(111)000...

   8    1    (1.000)000...

   9    7    0.00(1001)001...

  10    3    0.0(1010)101...

  11   11    0.000(1011)101...

  12    5    0.00(1100)110...

  13   19    0.0000(1101)011...

  14    9    0.000(1110)001...

  15   17    0.0000(1111)000...

  16    1    (1.0000)000...

  17   15    0.000(10001)000...

  18    7    0.00(10010)010...

  19   13    0.000(10011)101...

  20   25    0.0000(10100)011...

PROG

(PARI) See Links section.

CROSSREFS

Cf. A000975, A033138, A070939, A095156, A300428.

Sequence in context: A327968 A213815 A300428 * A143113 A053544 A174879

Adjacent sequences:  A300472 A300473 A300474 * A300476 A300477 A300478

KEYWORD

nonn,look,base

AUTHOR

Rémy Sigrist, Mar 06 2018

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 25 01:00 EDT 2022. Contains 354047 sequences. (Running on oeis4.)