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A115303
a(n) = n if n < 3, otherwise 3*a(floor(n/3)) + 2 - n mod 3.
11
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
1,2
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
FORMULA
a(n) = A115310(n+1,2).
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 *)
KEYWORD
nonn,base,look
AUTHOR
Reinhard Zumkeller, Jan 20 2006
STATUS
approved