login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A167489 Product of run lengths in binary representation of n. 13
1, 1, 1, 2, 2, 1, 2, 3, 3, 2, 1, 2, 4, 2, 3, 4, 4, 3, 2, 4, 2, 1, 2, 3, 6, 4, 2, 4, 6, 3, 4, 5, 5, 4, 3, 6, 4, 2, 4, 6, 3, 2, 1, 2, 4, 2, 3, 4, 8, 6, 4, 8, 4, 2, 4, 6, 9, 6, 3, 6, 8, 4, 5, 6, 6, 5, 4, 8, 6, 3, 6, 9, 6, 4, 2, 4, 8, 4, 6, 8, 4, 3, 2, 4, 2, 1, 2, 3, 6, 4, 2, 4, 6, 3, 4, 5, 10, 8, 6, 12, 8, 4, 8 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Antti Karttunen, Table of n, a(n) for n = 0..8192

FORMULA

a(n) = A227349(n) * A227350(n) = A227355(A227352(2n+1)). - Antti Karttunen, Jul 25 2013

EXAMPLE

a(99) = 12, because 99 in binary is written 1100011 giving the run lengths 2,3,2, and 2x3x2 = 12.

MATHEMATICA

Table[ Times @@ (Length /@ Split[IntegerDigits[n, 2]]), {n, 0, 100}](* Olivier Gérard, Jul 05 2013 *)

PROG

(Scheme)

(define (A167489 n) (apply * (binexp->runcount1list n)))

(define (binexp->runcount1list n) (if (zero? n) (list) (let loop ((n n) (rc (list)) (count 0) (prev-bit (modulo n 2))) (if (zero? n) (cons count rc) (if (eq? (modulo n 2) prev-bit) (loop (floor->exact (/ n 2)) rc (1+ count) (modulo n 2)) (loop (floor->exact (/ n 2)) (cons count rc) 1 (modulo n 2)))))))

;; Antti Karttunen, Jul 05 2013

(Haskell)

import Data.List (group)

a167489 = product . map length . group . a030308_row

-- Reinhard Zumkeller, Jul 05 2013

(Python)

def A167489(n):

  '''Product of run lengths in binary representation of n.'''

  p = 1

  b = n%2

  i = 0

  while (n != 0):

    n >>= 1

    i += 1

    if ((n%2) != b):

      p *= i

      i = 0

      b = n%2

  return(p)

# Antti Karttunen, Jul 24 2013 (Cf. Python program for A227184).

CROSSREFS

Cf. A167490 (smallest number with binary run length product = n).

Cf. A167491 (members of A167490 sorted in ascending order).

Cf. A227355, A227184, A227190.

Cf. A246588.

Sequence in context: A043276 A064742 A227185 * A256790 A256478 A106638

Adjacent sequences:  A167486 A167487 A167488 * A167490 A167491 A167492

KEYWORD

nonn,base

AUTHOR

Andrew Weimholt, Nov 05 2009

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy .

Last modified March 27 16:36 EDT 2017. Contains 284177 sequences.