login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A063005
Difference between 2^n and the next smaller or equal power of 3.
6
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
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. A000079 (2^n), A000244 (3^n), A136409.
Sequence in context: A177735 A139428 A303574 * A329763 A348727 A347901
KEYWORD
easy,nonn
AUTHOR
Jens Voß, Jul 02 2001
EXTENSIONS
More terms from Ralf Stephan, Mar 20 2003
STATUS
approved