A202821 Position of 6^n among 3-smooth numbers A003586.

1, 5, 14, 26, 43, 64, 89, 119, 153, 191, 233, 279, 330, 385, 444, 507, 575, 646, 722, 802, 886, 975, 1067, 1164, 1266, 1371, 1481, 1595, 1713, 1835, 1961, 2092, 2227, 2366, 2509, 2657, 2809, 2965, 3125, 3289, 3458, 3630, 3807, 3989, 4174, 4364, 4558, 4756

Offset: 0

Author

Zak Seidov, Dec 25 2011

Keywords

• nonn

Examples

			a(0) = 1 because A003586(1) = 6^0 = 1.
a(1) = 5 because A003586(5) = 6^1 = 6.
a(2) = 14 because A003586(14) = 6^2 = 36.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 0..10000 (terms 0..1000 from Zak Seidov)

Crossrefs

Cf. A000400, A003586, A022330, A022331.

Programs

Mathematica

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 *)

Python

# uses imports/function in A372401
print(list(islice(A372401gen(p=3), 1000))) # Michael S. Branicky, Jun 06 2024

Python

from sympy import integer_log
def A202821(n): return 1+n*(n+1)+sum((m:=3**i).bit_length()+((1<Chai Wah Wu, Oct 22 2024

Formula

A003586(a(n)) = 6^n, for n >= 0.

a(n) ~ (log(6))^2/(log(3)*log(4))*n^2 = 2.1079...*n^2.