A306835 - OEIS

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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.

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