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

0,2

Links

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

Formula

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

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

Example

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.

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 *)

Prog

(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<<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

Crossrefs

Cf. A000400, A003586, A022330, A022331.

Sequence in context: A070133 A246517 A306886 * A301689 A367690 A066479

Adjacent sequences: A202818 A202819 A202820 * A202822 A202823 A202824

Keyword

nonn

Author

Zak Seidov, Dec 25 2011

Status

approved