A063005 Difference between 2^n and the next smaller or equal power of 3.

0, 1, 1, 5, 7, 5, 37, 47, 13, 269, 295, 1319, 1909, 1631, 9823, 13085, 6487, 72023, 84997, 347141, 517135, 502829, 2599981, 3605639, 2428309, 19205525, 24062143, 5077565, 139295293, 149450423, 686321335, 985222181, 808182895, 5103150191, 6719515981, 2978678759

Offset

0,4

Comments

Sequence generalized : a(n) = A^n - B^(floor(log_B (A^n))) where A, B are integers. This sequence has A = 2, B = 3; A056577 has A = 3, B = 2. - Ctibor O. Zizka, Mar 03 2008

Links

Alois P. Heinz, Table of n, a(n) for n = 0..3324

Formula

a(n) = 2^n - 3^(floor (log_3 (2^n))).

a(n) = A000079(n) - 3^A136409(n). - Michel Marcus, Nov 19 2021

Maple

a:= n-> (t-> t-3^ilog[3](t))(2^n):
seq(a(n), n=0..40);  # Alois P. Heinz, Oct 11 2019

Mathematica

a[n_] := 2^n - 3^Floor[Log[3, 2] * n]; Array[a, 36, 0] (* Amiram Eldar, Nov 19 2021 *)

Prog

(PARI) for(n=0, 50, print1(2^n-3^floor(log(2^n)/log(3))", "))
(Python)
def a(n):
    m, p, target = 0, 1, 2**n
    while p <= target:  m += 1; p *= 3
    return target - 3**(m-1)
print([a(n) for n in range(36)]) # Michael S. Branicky, Nov 19 2021

Crossrefs

Cf. A056577, A063003, A063004.

Cf. A000079 (2^n), A000244 (3^n), A136409.

Sequence in context: A177735 A139428 A303574 * A329763 A348727 A347901

Adjacent sequences: A063002 A063003 A063004 * A063006 A063007 A063008

Keyword

easy,nonn

Author

Jens Voß, Jul 02 2001

Extensions

More terms from Ralf Stephan, Mar 20 2003

Status

approved