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A108238 Numbers of the form (7^i)*(12^j), with i, j >= 0.

%I A108238 #18 Apr 22 2025 03:59:43
%S A108238 1,7,12,49,84,144,343,588,1008,1728,2401,4116,7056,12096,16807,20736,
%T A108238 28812,49392,84672,117649,145152,201684,248832,345744,592704,823543,
%U A108238 1016064,1411788,1741824,2420208,2985984,4148928,5764801,7112448
%N A108238 Numbers of the form (7^i)*(12^j), with i, j >= 0.
%H A108238 Amiram Eldar, <a href="/A108238/b108238.txt">Table of n, a(n) for n = 1..10000</a>
%F A108238 Sum_{n>=1} 1/a(n) = (7*12)/((7-1)*(12-1)) = 14/11. - _Amiram Eldar_, Sep 26 2020
%F A108238 a(n) ~ exp(sqrt(2*log(7)*log(12)*n)) / sqrt(84). - _Vaclav Kotesovec_, Sep 26 2020
%t A108238 Take[7^#[[1]]*12^#[[2]]&/@Tuples[Range[0,10],2]//Union,40] (* _Harvey P. Dale_, Mar 05 2017 *)
%t A108238 n = 10^6; Flatten[Table[7^i*12^j, {i, 0, Log[7, n]}, {j, 0, Log[12, n/7^i]}]] // Sort (* _Amiram Eldar_, Sep 26 2020 *)
%o A108238 (Python)
%o A108238 from sympy import integer_log
%o A108238 def A108238(n):
%o A108238     def bisection(f,kmin=0,kmax=1):
%o A108238         while f(kmax) > kmax: kmax <<= 1
%o A108238         kmin = kmax >> 1
%o A108238         while kmax-kmin > 1:
%o A108238             kmid = kmax+kmin>>1
%o A108238             if f(kmid) <= kmid:
%o A108238                 kmax = kmid
%o A108238             else:
%o A108238                 kmin = kmid
%o A108238         return kmax
%o A108238     def f(x): return n+x-sum(integer_log(x//12**i,7)[0]+1 for i in range(integer_log(x,12)[0]+1))
%o A108238     return bisection(f,n,n) # _Chai Wah Wu_, Mar 26 2025
%Y A108238 Cf. A036566, A025631, A025632, A003599, A108056, A108201, A064476.
%K A108238 nonn,easy
%O A108238 1,2
%A A108238 Douglas Winston (douglas.winston(AT)srupc.com), Jun 17 2005