cp's OEIS Frontend

A317804 Numbers of form 2^i*12^j, with i, j >= 0.

%I A317804 #63 Apr 22 2025 05:08:42
%S A317804 1,2,4,8,12,16,24,32,48,64,96,128,144,192,256,288,384,512,576,768,
%T A317804 1024,1152,1536,1728,2048,2304,3072,3456,4096,4608,6144,6912,8192,
%U A317804 9216,12288,13824,16384,18432,20736,24576,27648,32768,36864,41472,49152,55296,65536
%N A317804 Numbers of form 2^i*12^j, with i, j >= 0.
%H A317804 Dario Ch, <a href="/A317804/b317804.txt">Table of n, a(n) for n = 1..10000</a>
%F A317804 Sum_{n>=1} 1/a(n) = 24/11. - _Amiram Eldar_, Mar 29 2025
%t A317804 With[{max = 10^5}, Flatten[Table[2^i*12^j, {i, 0, Log2[max]}, {j, 0, Log[12, max/2^i]}]] // Sort] (* _Amiram Eldar_, Mar 29 2025 *)
%o A317804 (Python)
%o A317804 from heapq import heappush, heappop
%o A317804 def sequence():
%o A317804     pq = [1]
%o A317804     seen = set(pq)
%o A317804     while True:
%o A317804         value = heappop(pq)
%o A317804         yield value
%o A317804         seen.remove(value)
%o A317804         for x in 2 * value, 12 * value:
%o A317804             if x not in seen:
%o A317804                 heappush(pq, x)
%o A317804                 seen.add(x)
%o A317804 seq = sequence()
%o A317804 finalsequence_list = [next(seq) for i in range(100)]  # _Dario Ch_, Sep 01 2018
%o A317804 (Python)
%o A317804 from sympy import integer_log
%o A317804 def A317804(n):
%o A317804     def bisection(f,kmin=0,kmax=1):
%o A317804         while f(kmax) > kmax: kmax <<= 1
%o A317804         kmin = kmax >> 1
%o A317804         while kmax-kmin > 1:
%o A317804             kmid = kmax+kmin>>1
%o A317804             if f(kmid) <= kmid:
%o A317804                 kmax = kmid
%o A317804             else:
%o A317804                 kmin = kmid
%o A317804         return kmax
%o A317804     def f(x): return n+x-sum((x//12**i).bit_length() for i in range(integer_log(x,12)[0]+1))
%o A317804     return bisection(f,n,n) # _Chai Wah Wu_, Mar 26 2025
%Y A317804 Cf. A025612, A003596, A107326, A003597, A107364, A025616, A108201, A108238.
%K A317804 nonn,easy
%O A317804 1,2
%A A317804 _Dario Ch_, Sep 01 2018