A115303 a(n) = n if n < 3, otherwise 3*a(floor(n/3)) + 2 - n mod 3.

1, 2, 5, 4, 3, 8, 7, 6, 17, 16, 15, 14, 13, 12, 11, 10, 9, 26, 25, 24, 23, 22, 21, 20, 19, 18, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 80, 79, 78, 77, 76, 75, 74, 73, 72, 71, 70, 69, 68, 67, 66, 65, 64, 63, 62

Offset: 1

Author

Reinhard Zumkeller, Jan 20 2006

Keywords

• nonn
• base
• look

Comments

Self-inverse permutation of the natural numbers.

if n is written in ternary representation, then a(n) is the value after replacing all digits d (but not the leading one) with 2-d.

a(n+1) = a(n)-1 unless n = 3^k - 1 or 2*3^k-1 for some k. - Robert Israel, Feb 28 2023

Links

• Robert Israel, Table of n, a(n) for n = 1..10000
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A054429, A115304, A115305, A115306, A115307, A115308, A115309, A106649.

Programs

Maple

a:= proc(n) option remember;
   3*procname(floor(n/3))+2 - (n mod 3)
end proc:
a(1):= 1: a(2):= 2:
map(a, [$1..100]); # Robert Israel, Feb 28 2023

Mathematica

A115303[n_] := FromDigits[MapAt[2 - # &, IntegerDigits[n, 3], 2;;], 3];
Array[A115303, 100] (* Paolo Xausa, May 20 2024 *)

Formula

a(n) = A115310(n+1,2).