A374484 - OEIS

A374484

Index of A006899(n) in A003586.

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

(list; graph; refs; listen; history; text; internal format)

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

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

Cf. A003586, A006899.

Disjoint union of A022330 and A022331.

Sequence in context: A304206 A243498 A156287 * A162293 A233459 A145803

Adjacent sequences: A374481 A374482 A374483 * A374485 A374486 A374487

KEYWORD

nonn,easy

AUTHOR

Chai Wah Wu, Sep 16 2024

STATUS

approved