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A202821
Position of 6^n among 3-smooth numbers A003586.
4
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
KEYWORD
nonn,changed
AUTHOR
Zak Seidov, Dec 25 2011
STATUS
approved