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

Author

Jens Voß, Jul 02 2001

Keywords

• easy
• nonn

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

Crossrefs

Cf. A056577, A063003, A063004.

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

Programs

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 *)

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

Formula

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

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

Extensions

More terms from Ralf Stephan, Mar 20 2003