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 A306835 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. 1
 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, 76, 39, 41, 43, 88, 45, 47, 96, 49, 100, 51, 53, 55, 112, 57, 59, 61, 124, 63, 65, 67, 136, 69, 71, 73, 148, 75, 77, 79, 160, 81, 83, 85, 172, 87, 89 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Jan Koornstra, Table of n, a(n) for n = 0..10000 David A. Corneth, PARI program EXAMPLE The first iterations of the sequence are as follows: [0, 1]; [0, 1, 2]; [0, 1, 3, 2], since 1 + 2 = 3; [0, 1, 4, 3, 2], since 1 + 3 = 4; [0, 1, 4, 3, 5, 2], since 3 + 2 = 5 (and appears later in the sequence than 1 + 4); [0, 1, 4, 3, 5, 2, 6]. MATHEMATICA 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 *) PROG (Python3) seq = [0, 1] for n in range(2, 281):   for k in range(len(seq) - 1, 0, -1):     if seq[k] + seq[k - 1] == n:       seq.insert(k, n)       break   else: seq += [n] print(seq[:100]) (PARI) See Corneth link \\ David A. Corneth, Mar 24 2019 CROSSREFS Sequence in context: A171021 A035427 A257120 * A033546 A236360 A299323 Adjacent sequences:  A306832 A306833 A306834 * A306836 A306837 A306838 KEYWORD nonn,easy AUTHOR Jan Koornstra, Mar 12 2019 STATUS approved

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Last modified September 28 17:43 EDT 2020. Contains 337393 sequences. (Running on oeis4.)