%I #36 Sep 16 2024 12:48:16
%S 1,2,1,3,2,4,1,3,5,2,4,1,6,3,5,2,7,4,1,6,3,8,5,2,7,4,1,9,6,3,8,5,2,10,
%T 7,4,1,9,6,3,11,8,5,2,10,7,4,12,1,9,6,3,11,8,5,13,2,10,7,4,12,1,9,6,
%U 14,3,11,8,5,13,2,10,7,15,4,12,1,9,6,14,3,11
%N Values of i in the numbers 2^i*3^j, i >= 1, j >= 1 (A033845).
%C Signature sequence of log_2(3) (A020857). - _R. J. Mathar_, May 27 2024
%H Zak Seidov, <a href="/A191475/b191475.txt">Table of n, a(n) for n = 1..10000</a>
%H <a href="/index/Si#signature_sequences">Index entries for sequences related to signature sequences</a>
%e a(10) = 2 because A033845(10) = 108 = 2^2*3^3.
%e a(100) = 2 because A033845(100) = 59872 = 2^8*3^7.
%e a(1000) = 56 because A033845(1000) = 216172782113783808 = 2^56*3^1.
%t mx = 1000000; t = Select[Sort[Flatten[Table[2^i 3^j, {i, Log[2, mx]}, {j, Log[3, mx]}]]], # <= mx &]; Table[FactorInteger[i][[1, 2]], {i, t}] (* _T. D. Noe_, Aug 31 2012 *)
%o (Python)
%o from sympy import integer_log
%o def A191475(n):
%o def bisection(f,kmin=0,kmax=1):
%o while f(kmax) > kmax: kmax <<= 1
%o while kmax-kmin > 1:
%o kmid = kmax+kmin>>1
%o if f(kmid) <= kmid:
%o kmax = kmid
%o else:
%o kmin = kmid
%o return kmax
%o def f(x): return n+x-sum((x//3**i).bit_length() for i in range(integer_log(x,3)[0]+1))
%o return 1+(~(m:=bisection(f,n,n))&m-1).bit_length() # _Chai Wah Wu_, Sep 15 2024
%Y Cf. A003586 (numbers 2^i*3^j, i >= 0, j >= 0), A033845 (numbers 2^i*3^j, i >= 1, j >= 1), A191476 (values of j), A020857.
%K nonn
%O 1,2
%A _Zak Seidov_, Aug 30 2012
%E Edited by _N. J. A. Sloane_, May 26 2024