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

1,3

Links

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

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

Example

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A000244, A365459.

Cf. also A062153, A064235, A080342.

Sequence in context: A343515 A351836 A105159 * A334625 A209291 A332875

Adjacent sequences: A365455 A365456 A365457 * A365459 A365460 A365461

Keyword

nonn

Author

Antti Karttunen, Sep 17 2023

Status

approved