A360281 - OEIS

%I #14 Jul 21 2024 11:36:25

%S 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,

%T 81,103,92,15,107,61,12,73,85,79,41,10,51,122,173,295,18,313,331,14,

%U 69,83,38,121,159,20,179,199,21,44,65,109,58,167,25,16,82,49

%N 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).

%C This sequence has similarities with A085947, A328444 and A332301:

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

%C - however, a(40) = 122,

%C      A085947(40) does not exist,

%C      A328444(40) = 34,

%C      A332301(40) = 61.

%H Rémy Sigrist, <a href="/A360281/b360281.txt">Table of n, a(n) for n = 1..10000</a>

%H Rémy Sigrist, <a href="/A360281/a360281.gp.txt">PARI program</a>.

%e The first terms, alongside the relationship with the two prior terms, are:

%e   n   a(n)  Relationship

%e   --  ----  ------------

%e    1     1  N/A

%e    2     2  N/A

%e    3     3  2+1

%e    4     5  3+2

%e    5     4  (5+3)/2

%e    6     9  4+5

%e    7    13  9+4

%e    8    11  (13+9)/2

%e    9     6  (11+13)/4

%e   10    17  6+11

%e   11    23  17+6

%e   12     8  (23+17)/5

%o (PARI) \\ See Links section.

%Y Cf. A085947, A328444, A332301.

%K nonn

%O 1,2

%A _Rémy Sigrist_, Feb 01 2023