This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
a(56) = 9, because 56 in binary is written 111000 giving the run lengths 3,3 and 3x3 = 9. a(99) = 12, because 99 in binary is written 1100011 giving the run lengths 2,3,2, and 2x3x2 = 12.
import Data.List (group) a167489 = product . map length . group . a030308_row -- Reinhard Zumkeller, Jul 05 2013
Table[ Times @@ (Length /@ Split[IntegerDigits[n, 2]]), {n, 0, 100}](* Olivier Gérard, Jul 05 2013 *)
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
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).
(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
For n = 27, in binary A007088(27) = "11011", the lengths of runs of 1-bits are [2,2], thus a(27) = lcm(2,2) = 2. For n = 55, in binary A007088(55) = "110111", the lengths of runs of 1-bits are [2,3], thus a(55) = lcm(2,3) = 6.
{0}~Join~Array[GCD @@ Map[Length, Split@ IntegerDigits[#, 2]] &, 104] (* Michael De Vlieger, Oct 17 2022 *)
a(n) = { my (r=[]); while (n, my (v=valuation(n+n%2, 2)); n\=2^v; r=concat(v, r)); gcd(r) }
from math import gcd
from itertools import groupby
def a(n):
if n == 0: return 0 # by convention
return gcd(*(len(list(g)) for k, g in groupby(bin(n)[2:])))
print([a(n) for n in range(87)]) # Michael S. Branicky, Oct 15 2022
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