cp's OEIS Frontend

A107466 Numbers of the form (5^i)*(13^j).

%I A107466 #22 Apr 22 2025 03:51:00
%S A107466 1,5,13,25,65,125,169,325,625,845,1625,2197,3125,4225,8125,10985,
%T A107466 15625,21125,28561,40625,54925,78125,105625,142805,203125,274625,
%U A107466 371293,390625,528125,714025,1015625,1373125,1856465,1953125,2640625
%N A107466 Numbers of the form (5^i)*(13^j).
%H A107466 Amiram Eldar, <a href="/A107466/b107466.txt">Table of n, a(n) for n = 1..10000</a>
%F A107466 Sum_{n>=1} 1/a(n) = (5*13)/((5-1)*(13-1)) = 65/48. - _Amiram Eldar_, Sep 23 2020
%F A107466 a(n) ~ exp(sqrt(2*log(5)*log(13)*n)) / sqrt(65). - _Vaclav Kotesovec_, Sep 23 2020
%t A107466 mx = 2700000; Sort@ Flatten@ Table[5^i*13^j, {i, 0, Log[5, mx]}, {j, 0, Log[13, mx/5^i]}] (* _Robert G. Wilson v_, Aug 17 2012 *)
%o A107466 (PARI) list(lim)=my(v=List(),N);for(n=0,log(lim)\log(13),N=13^n;while(N<=lim,listput(v,N);N*=5));vecsort(Vec(v)) \\ _Charles R Greathouse IV_, Jun 28 2011
%o A107466 (Python)
%o A107466 from sympy import integer_log
%o A107466 def A107466(n):
%o A107466     def bisection(f,kmin=0,kmax=1):
%o A107466         while f(kmax) > kmax: kmax <<= 1
%o A107466         kmin = kmax >> 1
%o A107466         while kmax-kmin > 1:
%o A107466             kmid = kmax+kmin>>1
%o A107466             if f(kmid) <= kmid:
%o A107466                 kmax = kmid
%o A107466             else:
%o A107466                 kmin = kmid
%o A107466         return kmax
%o A107466     def f(x): return n+x-sum(integer_log(x//13**i,5)[0]+1 for i in range(integer_log(x,13)[0]+1))
%o A107466     return bisection(f,n,n) # _Chai Wah Wu_, Mar 25 2025
%Y A107466 Cf. A003586, A003592, A003593, A003591, A003594, A003595, A003596, A003597, A003598, A003599, A107326, A107364.
%K A107466 nonn
%O A107466 1,2
%A A107466 Douglas Winston (douglas.winston(AT)srupc.com), May 27 2005