A360281 Lexicographically earliest sequence of distinct positive integers such that for any n > 2, a(n) is a divisor or a multiple of a(n-1) + a(n-2).

1, 2, 3, 5, 4, 9, 13, 11, 6, 17, 23, 8, 31, 39, 7, 46, 53, 33, 43, 19, 62, 27, 89, 29, 59, 22, 81, 103, 92, 15, 107, 61, 12, 73, 85, 79, 41, 10, 51, 122, 173, 295, 18, 313, 331, 14, 69, 83, 38, 121, 159, 20, 179, 199, 21, 44, 65, 109, 58, 167, 25, 16, 82, 49

Offset: 1

Author

Rémy Sigrist, Feb 01 2023

Keywords

• nonn

Comments

This sequence has similarities with A085947, A328444 and A332301:

- these sequences agree for n = 1..39,

- however, a(40) = 122,

A085947(40) does not exist,

A328444(40) = 34,

A332301(40) = 61.

Examples

			The first terms, alongside the relationship with the two prior terms, are:
  n   a(n)  Relationship
  --  ----  ------------
   1     1  N/A
   2     2  N/A
   3     3  2+1
   4     5  3+2
   5     4  (5+3)/2
   6     9  4+5
   7    13  9+4
   8    11  (13+9)/2
   9     6  (11+13)/4
  10    17  6+11
  11    23  17+6
  12     8  (23+17)/5
		

Links

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

Crossrefs

Cf. A085947, A328444, A332301.

Programs

PARI

\\ See Links section.