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A374484
Index of A006899(n) in A003586.
1
1, 2, 3, 4, 6, 7, 9, 12, 13, 17, 19, 22, 27, 28, 34, 37, 41, 48, 49, 56, 62, 65, 74, 77, 84, 93, 95, 106, 111, 118, 130, 131, 143, 152, 157, 171, 175, 186, 199, 202, 218, 225, 235, 252, 253, 271, 281, 290, 309, 312, 329, 344, 350, 371, 378, 393, 413, 416, 439
OFFSET
1,2
COMMENTS
Index of powers of 2 and 3 in 3-smooth numbers.
LINKS
FORMULA
A003586(a(n)) = A006899(n).
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
EXAMPLE
A006899(10) = 64 which is the 17th term of A003586, therefore a(10) = 17.
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
Disjoint union of A022330 and A022331.
Sequence in context: A304206 A243498 A156287 * A162293 A233459 A145803
KEYWORD
nonn,easy
AUTHOR
Chai Wah Wu, Sep 16 2024
STATUS
approved