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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).

%I A360281 #14 Jul 21 2024 11:36:25
%S A360281 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 A360281 81,103,92,15,107,61,12,73,85,79,41,10,51,122,173,295,18,313,331,14,
%U A360281 69,83,38,121,159,20,179,199,21,44,65,109,58,167,25,16,82,49
%N 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).
%C A360281 This sequence has similarities with A085947, A328444 and A332301:
%C A360281 - these sequences agree for n = 1..39,
%C A360281 - however, a(40) = 122,
%C A360281      A085947(40) does not exist,
%C A360281      A328444(40) = 34,
%C A360281      A332301(40) = 61.
%H A360281 Rémy Sigrist, <a href="/A360281/b360281.txt">Table of n, a(n) for n = 1..10000</a>
%H A360281 Rémy Sigrist, <a href="/A360281/a360281.gp.txt">PARI program</a>.
%e A360281 The first terms, alongside the relationship with the two prior terms, are:
%e A360281   n   a(n)  Relationship
%e A360281   --  ----  ------------
%e A360281    1     1  N/A
%e A360281    2     2  N/A
%e A360281    3     3  2+1
%e A360281    4     5  3+2
%e A360281    5     4  (5+3)/2
%e A360281    6     9  4+5
%e A360281    7    13  9+4
%e A360281    8    11  (13+9)/2
%e A360281    9     6  (11+13)/4
%e A360281   10    17  6+11
%e A360281   11    23  17+6
%e A360281   12     8  (23+17)/5
%o A360281 (PARI) \\ See Links section.
%Y A360281 Cf. A085947, A328444, A332301.
%K A360281 nonn
%O A360281 1,2
%A A360281 _Rémy Sigrist_, Feb 01 2023