cp's OEIS Frontend

A191475 Values of i in the numbers 2^i*3^j, i >= 1, j >= 1 (A033845).

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