%I #12 Dec 07 2016 10:36:12

%S 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,

%T 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,

%U 10,11,10,11,10,11,10,11,12,11,12,11,12,11,12,11,12,11,12,11,12,13,12,13

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

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

%C 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;

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

%H Reinhard Zumkeller, <a href="/A116939/b116939.txt">Table of n, a(n) for n = 0..10000</a>

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

%o (Haskell)

%o a116939 n = a116939_list !! n

%o a116939_list = 0 : f [0] where

%o f xs@(x : _) = ys ++ f ys where

%o ys = if odd x then (x + 1 : x : map (+ 1) xs) else map (+ 1) xs

%o -- _Reinhard Zumkeller_, Jun 28 2013

%K nonn

%O 0,3

%A _Reinhard Zumkeller_, Feb 27 2006