A036667 - OEIS

%I #28 Jan 31 2025 03:31:55

%S 1,4,6,9,16,24,36,54,64,81,96,144,216,256,324,384,486,576,729,864,

%T 1024,1296,1536,1944,2304,2916,3456,4096,4374,5184,6144,6561,7776,

%U 9216,11664,13824,16384,17496,20736,24576,26244,31104,36864,39366

%N Numbers of the form 2^i*3^j, i+j even.

%H Reinhard Zumkeller, <a href="/A036667/b036667.txt">Table of n, a(n) for n = 1..10000</a>

%F A069352(a(n)) mod 2 = 0. - _Reinhard Zumkeller_, May 16 2015

%F Sum_{n>=1} 1/a(n) = 7/4. - _Amiram Eldar_, Feb 18 2021

%t max = 40000;

%t Reap[Do[k = 2^i 3^j; If[k <= max && EvenQ[i+j], Sow[k]], {i, 0, Log[2, max] // Ceiling}, {j, 0, Log[3, max] // Ceiling}]][[2, 1]] // Union (* _Jean-François Alcover_, Aug 04 2018 *)

%o (Haskell)

%o a036667 n = a036667_list !! (n-1)

%o a036667_list = filter (even . flip mod 2 . a001222) a003586_list

%o -- _Reinhard Zumkeller_, May 16 2015

%o (Python)

%o from sympy import integer_log

%o def A036667(n):

%o     def bisection(f,kmin=0,kmax=1):

%o         while f(kmax) > kmax: kmax <<= 1

%o         kmin = 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()+(i&1^1)>>1 for i in range(integer_log(x, 3)[0]+1))

%o     return bisection(f,n,n) # _Chai Wah Wu_, Jan 30 2025

%Y Complement of A257999 with respect to A003586.

%Y Intersection of A028260 and A003586.

%Y Cf. A025620 (subsequence), A069352, A022328, A022329.

%K nonn

%O 1,2

%A _N. J. A. Sloane_

%E Offset corrected by _Reinhard Zumkeller_, May 16 2015