A022329 Exponent of 3 (value of j) in n-th number of form 2^i*3^j (see A003586).

0, 0, 1, 0, 1, 0, 2, 1, 0, 2, 1, 3, 0, 2, 1, 3, 0, 2, 4, 1, 3, 0, 2, 4, 1, 3, 5, 0, 2, 4, 1, 3, 5, 0, 2, 4, 6, 1, 3, 5, 0, 2, 4, 6, 1, 3, 5, 0, 7, 2, 4, 6, 1, 3, 5, 0, 7, 2, 4, 6, 1, 8, 3, 5, 0, 7, 2, 4, 6, 1, 8, 3, 5, 0, 7, 2, 9, 4, 6, 1, 8, 3, 5, 0, 7, 2, 9, 4, 6, 1, 8, 3, 10, 5, 0, 7, 2, 9, 4, 6, 1, 8, 3, 10, 5, 0, 7

Offset

1,7

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000 (first 1000 terms from Franklin T. Adams-Watters)

Formula

a(n) = A069352(n) - A022328(n). - Reinhard Zumkeller, May 16 2015

A003586(n) = 2^A022328(n) * 3^a(n). - N. J. A. Sloane, Mar 19 2009

a(n) = A191476(n) - 1. - Franklin T. Adams-Watters, Mar 19 2009

Mathematica

IntegerExponent[Select[Range[10^5], # == 2^IntegerExponent[#, 2] * 3^IntegerExponent[#, 3] &], 3] (* Amiram Eldar, Apr 15 2024 *)

Prog

(Haskell)
a022329 n = a022329_list !! (n-1)
-- Where a022329_list is defined in A022328.
-- Reinhard Zumkeller, Nov 19 2015, May 16 2015
(Python)
from sympy import integer_log
def A022329(n):
    def bisection(f, kmin=0, kmax=1):
        while f(kmax) > kmax: kmax <<= 1
        while kmax-kmin > 1:
            kmid = kmax+kmin>>1
            if f(kmid) <= kmid:
                kmax = kmid
            else:
                kmin = kmid
        return kmax
    def f(x): return n+x-sum((x//3**i).bit_length() for i in range(integer_log(x, 3)[0]+1))
    return integer_log((m:=bisection(f, n, n))>>(~m&m-1).bit_length(), 3)[0] # Chai Wah Wu, Sep 15 2024

Crossrefs

Cf. A003586, A022328, A191476. - Franklin T. Adams-Watters, Mar 19 2009

Cf. A069352.

Sequence in context: A025657 A025686 A215345 * A087466 A333211 A258033

Adjacent sequences: A022326 A022327 A022328 * A022330 A022331 A022332

Keyword

nonn

Author

Clark Kimberling

Extensions

Edited by N. J. A. Sloane, May 26 2024

Status

approved