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%I #19 Mar 31 2019 07:18:01
%S 0,1,4,3,5,7,16,9,11,24,13,15,17,19,40,21,23,25,27,29,31,64,33,35,37,
%T 76,39,41,43,88,45,47,96,49,100,51,53,55,112,57,59,61,124,63,65,67,
%U 136,69,71,73,148,75,77,79,160,81,83,85,172,87,89
%N a(0) = 0, a(1) = 1. For k > 1, k is inserted in the sequence between the last pair of consecutive terms already in the sequence which sum to k; if no such pair exists, k is added at the end of the sequence.
%H Jan Koornstra, <a href="/A306835/b306835.txt">Table of n, a(n) for n = 0..10000</a>
%H David A. Corneth, <a href="/A306835/a306835.gp.txt">PARI program</a>
%e The first iterations of the sequence are as follows:
%e [0, 1];
%e [0, 1, 2];
%e [0, 1, 3, 2], since 1 + 2 = 3;
%e [0, 1, 4, 3, 2], since 1 + 3 = 4;
%e [0, 1, 4, 3, 5, 2], since 3 + 2 = 5 (and appears later in the sequence than 1 + 4);
%e [0, 1, 4, 3, 5, 2, 6].
%t With[{nn = 270}, TakeWhile[Partition[Nest[Function[{a, n}, If[Length@ # == 0, Append[a, n], Insert[a, n, 1 + #[[-1, 1]] ]] &@ Position[Total /@ Partition[a, 2, 1], n] ] @@ {#, Length@ #} &, {0}, nn], 2, 1], Total@ # < nn &]][[All, 1]] (* _Michael De Vlieger_, Mar 24 2019 *)
%o (Python3)
%o seq = [0, 1]
%o for n in range(2, 281):
%o for k in range(len(seq) - 1, 0, -1):
%o if seq[k] + seq[k - 1] == n:
%o seq.insert(k, n)
%o break
%o else: seq += [n]
%o print(seq[:100])
%o (PARI) See Corneth link \\ _David A. Corneth_, Mar 24 2019
%K nonn,easy
%O 0,3
%A _Jan Koornstra_, Mar 12 2019
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