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.

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

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