A116939 Lexicographically earliest sequence such that each i occurs exactly i+1 times and succeeding terms differ exactly by -1 or +1.

0, 1, 2, 1, 2, 3, 2, 3, 4, 3, 4, 3, 4, 5, 4, 5, 4, 5, 6, 5, 6, 5, 6, 5, 6, 7, 6, 7, 6, 7, 6, 7, 8, 7, 8, 7, 8, 7, 8, 7, 8, 9, 8, 9, 8, 9, 8, 9, 8, 9, 10, 9, 10, 9, 10, 9, 10, 9, 10, 9, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 12, 11, 12, 11, 12, 11, 12, 11, 12, 11, 12, 11, 12, 13, 12, 13

Offset: 0

Author

Reinhard Zumkeller, Feb 27 2006

Keywords

• nonn

Comments

Permutation of A003056: a(n)=A003056(A116942(n)), a(A116941(n))=A003056(n);

for n>1: let x = number of occurrences of the most frequent term so far, a(n) = if x=a(n-1) then x+1 else x, a(1) = 1;

a(A000982(n))=a(A116940(n))=n, a(m)A000982(n) and a(m)>n for m>A000982(n).

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Programs

Haskell

a116939 n = a116939_list !! n
a116939_list = 0 : f [0] where
   f xs@(x : _) = ys ++ f ys where
     ys = if odd x then (x + 1 : x : map (+ 1) xs) else map (+ 1) xs
-- Reinhard Zumkeller, Jun 28 2013

Mathematica

a = {0}; Do[AppendTo[a, If[Count[a, # - 1] > # - 1, # + 1, # - 1]] &@ a[[n]], {n, 87}]; a (* Michael De Vlieger, Dec 07 2016 *)