A281409 Lexicographically first sequence of distinct terms, beginning with a(1)=5, with the property that each triple of consecutive terms contains a term that divides the sum of the other two terms.

5, 1, 2, 3, 4, 7, 9, 8, 10, 6, 14, 16, 12, 20, 28, 24, 13, 11, 15, 18, 21, 33, 27, 30, 19, 41, 22, 25, 47, 36, 58, 50, 42, 23, 61, 31, 32, 63, 65, 64, 43, 85, 44, 91, 45, 17, 40, 57, 74, 97, 51, 37, 60, 83, 106, 129, 152, 175, 109, 66, 35, 39, 82, 113, 133, 93

Offset

1,1

Comments

The initial term a(1)=5 seems to be the least one that leads to a sequence that is not ultimately linear.

The variant with:

- a(1)=1 matches A000027,

- a(1)=2 matches A181440,

- a(1)=3 starts with 3, 1, 2, and then matches A000027,

- a(1)=4 starts with 4, 1, 2, and then matches A143097,

- a(1)=6 starts with 6, 1, 2, 3, 4, 5, and then matches A000027,

- a(1)=9 starts with 9, 1, 2, 3, 4, 5, 6, 7, 8, 13, 11, 12, 10, and then matches A143097.

Conjecturally, all other variants are not ultimately linear.

Links

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Rémy Sigrist, PARI program for A281409

Example

The first terms, alongside the indexes of the terms that divide the sum of the other two terms within the n-th triple of consecutive terms, are:
   n  a(n)   Indexes
  --  ----   -------
   1    5    2, 3
   2    1    1, 2, 3
   3    2    2
   4    3    3
   5    4    1
   6    7    3
   7    9    1
   8    8    1, 3
   9   10    1, 2
  10    6    1
  11   14    1
  12   16    1, 2
  13   12    1, 2
  14   20    3
  15   28    3
  16   24    1
  17   13    1
  18   11    1
  19   15    2
  20   18    1
  21   21    3
  22   33    3
  23   27    3
  24   30    1
  25   19    2

Crossrefs

Cf. A000027, A143097, A181440, A278962, A281408.

Sequence in context: A029762 A222214 A055185 * A120579 A093316 A085758

Adjacent sequences: A281406 A281407 A281408 * A281410 A281411 A281412

Keyword

nonn

Author

Rémy Sigrist, Jan 21 2017

Status

approved