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A108056 Numbers of the form (7^i)*(13^j).

%I A108056 #16 Oct 22 2024 15:12:21
%S A108056 1,7,13,49,91,169,343,637,1183,2197,2401,4459,8281,15379,16807,28561,
%T A108056 31213,57967,107653,117649,199927,218491,371293,405769,753571,823543,
%U A108056 1399489,1529437,2599051,2840383,4826809,5274997,5764801,9796423,10706059,18193357,19882681
%N A108056 Numbers of the form (7^i)*(13^j).
%H A108056 Amiram Eldar, <a href="/A108056/b108056.txt">Table of n, a(n) for n = 1..10000</a>
%F A108056 Sum_{n>=1} 1/a(n) = (7*13)/((7-1)*(13-1)) = 91/72. - _Amiram Eldar_, Sep 23 2020
%F A108056 a(n) ~ exp(sqrt(2*log(7)*log(13)*n)) / sqrt(91). - _Vaclav Kotesovec_, Sep 23 2020
%t A108056 n = 10^7; Flatten[Table[7^i*13^j, {i, 0, Log[7, n]}, {j, 0, Log[13, n/7^i]}]] // Sort (* _Amiram Eldar_, Sep 23 2020 *)
%o A108056 (PARI) list(lim)=my(v=List(),N);for(n=0,log(lim)\log(13),N=13^n;while(N<=lim,listput(v,N);N*=7));vecsort(Vec(v)) \\ _Charles R Greathouse IV_, Jun 28 2011
%o A108056 (Python)
%o A108056 from sympy import integer_log
%o A108056 def A108056(n):
%o A108056     def bisection(f,kmin=0,kmax=1):
%o A108056         while f(kmax) > kmax: kmax <<= 1
%o A108056         while kmax-kmin > 1:
%o A108056             kmid = kmax+kmin>>1
%o A108056             if f(kmid) <= kmid:
%o A108056                 kmax = kmid
%o A108056             else:
%o A108056                 kmin = kmid
%o A108056         return kmax
%o A108056     def f(x): return n+x-sum(integer_log(x//13**i,7)[0]+1 for i in range(integer_log(x,13)[0]+1))
%o A108056     return bisection(f,n,n) # _Chai Wah Wu_, Oct 22 2024
%Y A108056 Cf. A003586, A003592, A003593, A003591, A003594, A003595, A003596, A003597, A003598, A003599, A107326, A107364, A107466.
%K A108056 nonn,easy
%O A108056 1,2
%A A108056 Douglas Winston (douglas.winston(AT)srupc.com), Jun 02 2005
%E A108056 More terms from _Amiram Eldar_, Sep 23 2020