cp's OEIS Frontend

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.

%I A281409 #16 Jan 22 2017 21:35:40
%S A281409 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,
%T A281409 22,25,47,36,58,50,42,23,61,31,32,63,65,64,43,85,44,91,45,17,40,57,74,
%U A281409 97,51,37,60,83,106,129,152,175,109,66,35,39,82,113,133,93
%N 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.
%C A281409 The initial term a(1)=5 seems to be the least one that leads to a sequence that is not ultimately linear.
%C A281409 The variant with:
%C A281409 - a(1)=1 matches A000027,
%C A281409 - a(1)=2 matches A181440,
%C A281409 - a(1)=3 starts with 3, 1, 2, and then matches A000027,
%C A281409 - a(1)=4 starts with 4, 1, 2, and then matches A143097,
%C A281409 - a(1)=6 starts with 6, 1, 2, 3, 4, 5, and then matches A000027,
%C A281409 - a(1)=9 starts with 9, 1, 2, 3, 4, 5, 6, 7, 8, 13, 11, 12, 10, and then matches A143097.
%C A281409 Conjecturally, all other variants are not ultimately linear.
%H A281409 Rémy Sigrist, <a href="/A281409/b281409.txt">Table of n, a(n) for n = 1..10000</a>
%H A281409 Rémy Sigrist, <a href="/A281409/a281409.gp.txt">PARI program for A281409</a>
%e A281409 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:
%e A281409    n  a(n)   Indexes
%e A281409   --  ----   -------
%e A281409    1    5    2, 3
%e A281409    2    1    1, 2, 3
%e A281409    3    2    2
%e A281409    4    3    3
%e A281409    5    4    1
%e A281409    6    7    3
%e A281409    7    9    1
%e A281409    8    8    1, 3
%e A281409    9   10    1, 2
%e A281409   10    6    1
%e A281409   11   14    1
%e A281409   12   16    1, 2
%e A281409   13   12    1, 2
%e A281409   14   20    3
%e A281409   15   28    3
%e A281409   16   24    1
%e A281409   17   13    1
%e A281409   18   11    1
%e A281409   19   15    2
%e A281409   20   18    1
%e A281409   21   21    3
%e A281409   22   33    3
%e A281409   23   27    3
%e A281409   24   30    1
%e A281409   25   19    2
%Y A281409 Cf. A000027, A143097, A181440, A278962, A281408.
%K A281409 nonn
%O A281409 1,1
%A A281409 _Rémy Sigrist_, Jan 21 2017