This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A202821 #38 Oct 23 2024 00:43:11
%S A202821 1,5,14,26,43,64,89,119,153,191,233,279,330,385,444,507,575,646,722,
%T A202821 802,886,975,1067,1164,1266,1371,1481,1595,1713,1835,1961,2092,2227,
%U A202821 2366,2509,2657,2809,2965,3125,3289,3458,3630,3807,3989,4174,4364,4558,4756
%N A202821 Position of 6^n among 3-smooth numbers A003586.
%H A202821 Amiram Eldar, <a href="/A202821/b202821.txt">Table of n, a(n) for n = 0..10000</a> (terms 0..1000 from Zak Seidov)
%F A202821 A003586(a(n)) = 6^n, for n >= 0.
%F A202821 a(n) ~ (log(6))^2/(log(3)*log(4))*n^2 = 2.1079...*n^2.
%e A202821 a(0) = 1 because A003586(1) = 6^0 = 1.
%e A202821 a(1) = 5 because A003586(5) = 6^1 = 6.
%e A202821 a(2) = 14 because A003586(14) = 6^2 = 36.
%t A202821 a[n_] := Sum[Floor[Log[3, 6^n/2^i]] + 1, {i, 0, Log2[6^n]}]; Array[a, 50, 0] (* _Amiram Eldar_, Jul 15 2023 *)
%o A202821 (Python) # uses imports/function in A372401
%o A202821 print(list(islice(A372401gen(p=3), 1000))) # _Michael S. Branicky_, Jun 06 2024
%o A202821 (Python)
%o A202821 from sympy import integer_log
%o A202821 def A202821(n): return 1+n*(n+1)+sum((m:=3**i).bit_length()+((1<<n)//m).bit_length() for i in range(1,integer_log(1<<n,3)[0]+1))+sum((3**i).bit_length() for i in range(integer_log(1<<n,3)[0]+1,n+1)) # _Chai Wah Wu_, Oct 22 2024
%Y A202821 Cf. A000400, A003586, A022330, A022331.
%K A202821 nonn
%O A202821 0,2
%A A202821 _Zak Seidov_, Dec 25 2011