A064515 Write A064476(n) = 2^i(n)*3^j(n); sequence gives values of j(n).

0, 1, 1, 2, 2, 2, 3, 3, 3, 4, 3, 4, 4, 5, 4, 5, 4, 5, 6, 5, 6, 5, 6, 5, 7, 6, 7, 6, 7, 6, 8, 7, 6, 8, 7, 8, 7, 9, 8, 7, 9, 8, 7, 9, 8, 10, 9, 8, 10, 9, 8, 10, 9, 11, 8, 10, 9, 11, 10, 9, 11, 10, 12, 9, 11, 10, 12, 9, 11, 10, 12, 11, 13, 10, 12, 11, 13, 10, 12, 11, 13, 10, 12, 14, 11, 13, 12

Offset: 1

Author

Vladeta Jovovic, Oct 07 2001, Oct 07 2001

Keywords

• nonn
• easy

Crossrefs

Cf. A064476, A064514.

Programs

ARIBAS

function a064515(maxarg: integer); var j: integer; ar: array; begin ar := p2p3(maxarg); for j := 0 to maxarg - 1 do write(ar[j][2]," "); end; end; a064515(95);  (* For definition of function p2p3 see A064476. *)

Python

from sympy import integer_log
def A064515(n):
    def bisection(f,kmin=0,kmax=1):
        while f(kmax) > kmax: kmax <<= 1
        kmin = 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(max(0,min((i<<1)+1,(x//3**i).bit_length())-i) for i in range(integer_log(x,3)[0]+1))
    return integer_log((m:=bisection(f,n,n))>>(m-1&~m).bit_length(),3)[0] # Chai Wah Wu, Mar 26 2025

Extensions

More terms from Klaus Brockhaus, Oct 12 2001