|
%I #36 Apr 17 2017 09:01:49
%S 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,
%T 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,
%U 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
%N Product of run lengths in binary representation of n.
%H Antti Karttunen, <a href="/A167489/b167489.txt">Table of n, a(n) for n = 0..8192</a>
%H <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%F a(n) = A227349(n) * A227350(n) = A227355(A227352(2n+1)). - _Antti Karttunen_, Jul 25 2013
%F a(n) = A284558(n) * A284559(n) = A284582(n) * A284583(n). - _Antti Karttunen_, Apr 16 2017
%e a(56) = 9, because 56 in binary is written 111000 giving the run lengths 3,3 and 3x3 = 9.
%e a(99) = 12, because 99 in binary is written 1100011 giving the run lengths 2,3,2, and 2x3x2 = 12.
%t Table[ Times @@ (Length /@ Split[IntegerDigits[n, 2]]), {n, 0, 100}](* _Olivier Gérard_, Jul 05 2013 *)
%o (Scheme)
%o (define (A167489 n) (apply * (binexp->runcount1list n)))
%o (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)))))))
%o ;; _Antti Karttunen_, Jul 05 2013
%o (Haskell)
%o import Data.List (group)
%o a167489 = product . map length . group . a030308_row
%o -- _Reinhard Zumkeller_, Jul 05 2013
%o (Python)
%o def A167489(n):
%o '''Product of run lengths in binary representation of n.'''
%o p = 1
%o b = n%2
%o i = 0
%o while (n != 0):
%o n >>= 1
%o i += 1
%o if ((n%2) != b):
%o p *= i
%o i = 0
%o b = n%2
%o return(p)
%o # _Antti Karttunen_, Jul 24 2013 (Cf. Python program for A227184).
%o (PARI) a(n) = {my(p=1, b=n%2, i=0); while(n!=0, n=n>>1; i=i+1; if((n%2)!=b, p=p*i; i=0; b=n%2)); p} \\ _Indranil Ghosh_, Apr 17 2017, after the Python Program by _Antti Karttunen_
%Y Row products of A101211 and A227736 (for n > 0).
%Y Cf. A167490 (smallest number with binary run length product = n).
%Y Cf. A167491 (members of A167490 sorted in ascending order).
%Y Cf. A227355, A227184, A227190.
%Y Cf. A227349, A227350, A227352, A246588, A284558, A284559, A284582, A284583.
%Y Differs from similar A284579 for the first time at n=56, where a(56) = 9, while A284579(56) = 5.
%K nonn,base
%O 0,4
%A _Andrew Weimholt_, Nov 05 2009
|
