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A064514 Write A064476(n) = 2^i(n)*3^j(n); sequence gives values of i(n).

%I A064514 #17 Apr 22 2025 02:16:32
%S A064514 0,1,2,2,3,4,3,4,5,4,6,5,6,5,7,6,8,7,6,8,7,9,8,10,7,9,8,10,9,11,8,10,
%T A064514 12,9,11,10,12,9,11,13,10,12,14,11,13,10,12,14,11,13,15,12,14,11,16,
%U A064514 13,15,12,14,16,13,15,12,17,14,16,13,18,15,17,14,16,13,18,15,17,14,19,16
%N A064514 Write A064476(n) = 2^i(n)*3^j(n); sequence gives values of i(n).
%o A064514 (ARIBAS) function a064514(maxarg: integer); var j: integer; ar: array; begin ar := p2p3(maxarg); for j := 0 to maxarg - 1 do write(ar[j][1]," "); end; end; a064514(85);  (* For definition of function p2p3 see A064476. *)
%o A064514 (Python)
%o A064514 from sympy import integer_log
%o A064514 def A064514(n):
%o A064514     def bisection(f,kmin=0,kmax=1):
%o A064514         while f(kmax) > kmax: kmax <<= 1
%o A064514         kmin = kmax >> 1
%o A064514         while kmax-kmin > 1:
%o A064514             kmid = kmax+kmin>>1
%o A064514             if f(kmid) <= kmid:
%o A064514                 kmax = kmid
%o A064514             else:
%o A064514                 kmin = kmid
%o A064514         return kmax
%o A064514     def f(x): return n+x-sum(max(0,min((i<<1)+1,(x//3**i).bit_length())-i) for i in range(integer_log(x,3)[0]+1))
%o A064514     return ((m:=bisection(f,n,n))-1&~m).bit_length() # _Chai Wah Wu_, Mar 26 2025
%Y A064514 Cf. A064476, A064515.
%K A064514 nonn,easy
%O A064514 1,3
%A A064514 _Vladeta Jovovic_, Oct 07 2001
%E A064514 More terms from _Klaus Brockhaus_, Oct 12 2001