A270755 a(1) = 1; a(n) = min{(n-1-a(n-1));(n-1-i)}, where i (0<=i<=n-2) is the largest number such that a(n-1)=a(i) or i=0 if no such a(i) exists.

1, 0, 2, 1, 3, 2, 3, 2, 2, 1, 6, 5, 7, 6, 3, 8, 8, 1, 8, 2, 11, 10, 12, 11, 3, 10, 4, 23, 5, 17, 13, 18, 14, 19, 15, 20, 16, 21, 17, 9, 31, 10, 16, 6, 30, 15, 11, 23, 20, 13, 19, 17, 13, 3, 29, 26, 30, 12, 35, 24, 36, 25, 37, 26, 8, 46, 20, 18, 36, 8, 5, 42, 30, 16, 31, 34, 42, 5, 7, 66, 14, 48, 34, 49, 35, 26, 30, 14, 7, 10, 48, 9, 52, 41, 53, 42, 19, 63, 35, 14

Offset

1,3

Comments

Sum_{i=1..n} a(n) ~ n*(n+1)/5.

Links

Table of n, a(n) for n=1..100.

Example

a(1) = 1;
a(2) = min{(1-1);(1-0)} = 0;
a(3) = min{(2-0);(2-0)} = 2;
a(4) = min{(3-2);(3-0)} = 1;
a(5) = min{(4-1);(4-1)} = 3;
a(6) = min{(5-3);(5-0)} = 2;
a(7) = min{(6-2);(6-3)} = 3;
a(8) = min{(7-3);(7-5)} = 2;
a(9) = min{(8-2);(8-6)} = 2;
a(10) = min{(9-2);(9-8)} = 1;
and so on.

Mathematica

a = {1}; Do[AppendTo[a, Min[n - 1 - a[[n - 1]], n - 1 - (If[MissingQ@#, 0, #] &@ SelectFirst[Range[n - 2, 1, -1], a[[n - 1]] == a[[#]] &])]], {n, 2, 120}]; a (* Michael De Vlieger, Mar 27 2016, Version 10.2 *)

Crossrefs

Cf. A181391, A267794, A268584.

Sequence in context: A334523 A001480 A308117 * A305030 A110917 A329340

Adjacent sequences: A270752 A270753 A270754 * A270756 A270757 A270758

Keyword

nonn

Author

Ctibor O. Zizka, Mar 22 2016

Status

approved