A365459 a(n) = n - the largest power of 3 that is less than or equal to n.

0, 1, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 0, 1, 2, 3, 4, 5, 6, 7

Offset

1,5

Links

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

Formula

a(n) = n - A365458(n).

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

Mathematica

Array[# - 3^Floor@ Log[3, #] &, 88] (* Michael De Vlieger, Sep 17 2023 *)

Prog

(PARI) A365459(n) = if(1==n, 0, my(k=0); while((3^k) < n, k++); if((3^k) > n, k--); n-(3^k));
(Python)
def A365459(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 n-3**kmin # Chai Wah Wu, Sep 17 2023

Crossrefs

Cf. A000244, A053735 (gives the number of iterations needed to reach 0), A365458.

Sequence in context: A260187 A257687 A309957 * A220660 A257846 A203572

Adjacent sequences: A365456 A365457 A365458 * A365460 A365461 A365462

Keyword

nonn

Author

Antti Karttunen, Sep 17 2023

Status

approved