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A372400 Position of 30^n among 5-smooth numbers A051037.

%I A372400 #15 Sep 19 2024 16:02:22
%S A372400 1,18,83,228,486,888,1466,2255,3283,4583,6189,8134,10445,13158,16305,
%T A372400 19916,24027,28667,33870,39665,46086,53166,60937,69429,78675,88709,
%U A372400 99561,111263,123849,137347,151793,167219,183658,201139,219695,239359,260165,282141,305320
%N A372400 Position of 30^n among 5-smooth numbers A051037.
%C A372400 Also position of 30^(n+1) in A143207.
%H A372400 Charles R Greathouse IV, <a href="/A372400/b372400.txt">Table of n, a(n) for n = 0..1000</a>
%F A372400 a(n) = k*n^3 + (3k/2)*n^2 + O(n) where k = (log 30)^3/(6 log 2 log 3 log 5) = 5.35057081984.... - _Charles R Greathouse IV_, Sep 19 2024
%t A372400 Table[Sum[Floor@ Log[5, 30^n/(2^i*3^j)] + 1, {i, 0, Log[2, 30^n]}, {j, 0, Log[3, 30^n/2^i]}], {n, 0, 38}]
%o A372400 (Python) # uses imports/function in A372401
%o A372400 print(list(islice(A372401gen(p=5), 40))) # _Michael S. Branicky_, Jun 05 2024
%o A372400 (Python)
%o A372400 from sympy import integer_log
%o A372400 def A372400(n):
%o A372400     c, x = 0, 30**n
%o A372400     for i in range(integer_log(x,5)[0]+1):
%o A372400         for j in range(integer_log(y:=x//5**i,3)[0]+1):
%o A372400             c += (y//3**j).bit_length()
%o A372400     return c # _Chai Wah Wu_, Sep 16 2024
%o A372400 (PARI) a(n)=my(t=30^n,u=5*t); sum(a=0,logint(t,5), u\=5; sum(b=0,logint(u,3), logint(u\3^b,2)+1)) \\ _Charles R Greathouse IV_, Sep 18 2024
%Y A372400 Cf. A002110, A051037, A143207, A202821, A372401, A372402.
%K A372400 nonn
%O A372400 0,2
%A A372400 _Michael De Vlieger_, Jun 03 2024