A365458 The largest power of 3 that is less than or equal to n.

1, 1, 3, 3, 3, 3, 3, 3, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 81, 81, 81, 81, 81

Offset: 1

Author

Antti Karttunen, Sep 17 2023

Keywords

• nonn

Examples

			a(2) = 1 because 3^0 = 1 <= 2.
a(3) = 3 because 3^1 = 3 <= 3.
a(4) = 3 because 3^1 = 3 <= 4.
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..19683 (3^9 = 19683)

Crossrefs

Cf. A000244, A365459.

Cf. also A062153, A064235, A080342.

Programs

Mathematica

Array[3^Floor@ Log[3, #] &, 90] (* Michael De Vlieger, Sep 17 2023 *)

PARI

A365458(n) = if(1==n,n,my(k=0); while((3^k) < n, k++); if((3^k) > n,k--); (3^k));

PARI

a(n) = 3^logint(n, 3); \\ Michel Marcus, Sep 17 2023

Python

def A365458(n):
    kmin, kmax = 0, 1
    while 3**kmax <= n:
        kmax <<= 1
    while True:
        kmid = kmax+kmin>>1
        if 3**kmid > n:
            kmax = kmid
        else:
            kmin = kmid
        if kmax-kmin <= 1:
            break
    return 3**kmin # Chai Wah Wu, Sep 17 2023

Formula

a(n) = 3^floor((log n) / (log 3)). - Michael De Vlieger, Sep 17 2023

a(n) = A000244(A062153(n)). - Michel Marcus, Sep 17 2023