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

Author

Antti Karttunen, Jul 29 2009

Keywords

• nonn
• base
• look

Examples

			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.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 0..728
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A007089, A163328-A163329.

Other bases: A057300, A126006, A217558.

Programs

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

Scheme

(define (A163327 n) (+ (A037314 (A163326 n)) (* 3 (A037314 (A163325 n)))))

Formula

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

Extensions

Edited by Charles R Greathouse IV, Nov 01 2009