OFFSET
1,2
COMMENTS
Index of powers of 2 and 3 in 3-smooth numbers.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
FORMULA
a(n) ~ c * n^2, where c = log(2)*log(3)/(2*(log(2) + log(3))^2) = 0.118598856384648... - Vaclav Kotesovec and Amiram Eldar, Sep 19 2024
MATHEMATICA
seq[lim_] := Position[Times @@ IntegerExponent[#, {2, 3}] & /@ Sort[Flatten[ Table[2^i*3^j, {i, 0, Log2[lim]}, {j, 0, Log[3, lim/2^i]}] ]], 0] // Flatten; seq[10^11] (* Amiram Eldar, Sep 18 2024 *)
PROG
(Python)
from sympy import integer_log
def A374484(n): return sum(((1<<k)//3**i).bit_length() for i in range(integer_log(1<<k, 3)[0]+1)) if integer_log(m:=3**(n-1), 6)[0]<(k:=integer_log(3*m, 6)[0]) else sum((3**i).bit_length() for i in range(integer_log(1<<n, 6)[0]+1))
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Chai Wah Wu, Sep 16 2024
STATUS
approved