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!)
A306549 a(n) is the product of the positions of the zeros in the binary expansion of n (the most significant bit having position 1). 2
1, 1, 2, 1, 6, 2, 3, 1, 24, 6, 8, 2, 12, 3, 4, 1, 120, 24, 30, 6, 40, 8, 10, 2, 60, 12, 15, 3, 20, 4, 5, 1, 720, 120, 144, 24, 180, 30, 36, 6, 240, 40, 48, 8, 60, 10, 12, 2, 360, 60, 72, 12, 90, 15, 18, 3, 120, 20, 24, 4, 30, 5, 6, 1, 5040, 720, 840, 120, 1008 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Apparently, the variant where the least significant bit has position 1 corresponds to A124773.

LINKS

Rémy Sigrist, Table of n, a(n) for n = 0..16384

FORMULA

a(n) = A070939(n)! / A306286(n).

a(2*n) = a(n) * (1+A070939(n)).

a(2*n+1) = a(n).

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

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

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

EXAMPLE

The first terms, alongside the positions of zeros and the binary representation of n, are:

  n   a(n)  Pos.zeros  bin(n)

  --  ----  ---------  ------

   0     1  {1}             0

   1     1  {}              1

   2     2  {2}            10

   3     1  {}             11

   4     6  {2,3}         100

   5     2  {2}           101

   6     3  {3}           110

   7     1  {}            111

   8    24  {2,3,4}      1000

   9     6  {2,3}        1001

  10     8  {2,4}        1010

  11     2  {2}          1011

  12    12  {3,4}        1100

  13     3  {3}          1101

  14     4  {4}          1110

  15     1  {}           1111

PROG

(PARI) a(n) = my (b=binary(n)); prod(k=1, #b, if (b[k]==0, k, 1))

CROSSREFS

Cf. A070939, A124773, A306286.

Sequence in context: A325815 A292441 A333726 * A198870 A050457 A195441

Adjacent sequences:  A306546 A306547 A306548 * A306550 A306551 A306552

KEYWORD

nonn,base,easy

AUTHOR

Rémy Sigrist, May 04 2019

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 24 18:27 EDT 2022. Contains 354043 sequences. (Running on oeis4.)