A163327 Self-inverse permutation of integers: swap the odd- and even-positioned digits in the ternary expansion of n, then convert back to decimal.

0, 3, 6, 1, 4, 7, 2, 5, 8, 27, 30, 33, 28, 31, 34, 29, 32, 35, 54, 57, 60, 55, 58, 61, 56, 59, 62, 9, 12, 15, 10, 13, 16, 11, 14, 17, 36, 39, 42, 37, 40, 43, 38, 41, 44, 63, 66, 69, 64, 67, 70, 65, 68, 71, 18, 21, 24, 19, 22, 25, 20, 23, 26, 45, 48, 51, 46, 49, 52, 47, 50, 53

Offset

0,2

Links

Antti Karttunen, Table of n, a(n) for n = 0..728

Index entries for sequences that are permutations of the natural numbers

Formula

a(n) = A037314(A163326(n)) + 3*A037314(A163325(n))

Example

11 in ternary base (A007089) is written as '(000...)102' (... + 0*27 + 1*9 + 0*3 + 2), which results '1020' = 1*27 + 0*9 + 2*3 + 0 = 33, when the odd- and even-positioned digits are swapped, thus a(11) = 33.

Prog

(Scheme) (define (A163327 n) (+ (A037314 (A163326 n)) (* 3 (A037314 (A163325 n)))))
(Python)
from sympy.ntheory import digits
def a(n):
    d = digits(n, 3)[1:]
    return sum(3**(i+(1-2*(i&1)))*di for i, di in enumerate(d[::-1]))
print([a(n) for n in range(72)]) # Michael S. Branicky, Aug 05 2022

Crossrefs

Cf. A007089, A163328-A163329.

Other bases: A057300, A126006, A217558.

Sequence in context: A199795 A200358 A181099 * A338460 A175032 A078768

Adjacent sequences: A163324 A163325 A163326 * A163328 A163329 A163330

Keyword

nonn,base,look

Author

Antti Karttunen, Jul 29 2009

Extensions

Edited by Charles R Greathouse IV, Nov 01 2009

Status

approved