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A328444 Lexicographically earliest sequence of distinct positive numbers such that a(1) = 1, a(2) = 2, and for n > 2, a(n) divides Sum_{i = n-k..n-1} a(i) with k > 0 as small as possible.

%I A328444 #20 Aug 23 2024 15:04:48
%S A328444 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 A328444 81,103,92,15,107,61,12,73,85,79,41,10,51,34,95,129,14,143,157,20,177,
%U A328444 197,187,16,203,219,211,86,99,37,68,21,18,24,42,66,36,102
%N A328444 Lexicographically earliest sequence of distinct positive numbers such that a(1) = 1, a(2) = 2, and for n > 2, a(n) divides Sum_{i = n-k..n-1} a(i) with k > 0 as small as possible.
%C A328444 When computing a(n) for n > 2, there may be candidates for different values of k; we choose the candidate that minimizes k.
%C A328444 This sequence is an infinite variant of A085947; a(n) = A085947(n) for n = 1..39.
%H A328444 Rémy Sigrist, <a href="/A328444/b328444.txt">Table of n, a(n) for n = 1..10000</a>
%H A328444 Rémy Sigrist, <a href="/A328444/a328444.gp.txt">PARI program for A328444</a>
%F A328444 a(n) <= Sum_{k = 1..n-1} a(k) for any n > 2.
%e A328444 For n = 3:
%e A328444 - the divisors of a(2) = 2 are all already in the sequence,
%e A328444 - 3 is the least divisor of a(1) + a(2) = 1 + 2 = 3 not yet in the sequence,
%e A328444 - so a(3) = 3.
%e A328444 For n = 4:
%e A328444 - the divisors of a(3) = 3 are all already in the sequence,
%e A328444 - 5 is the least divisor of a(2) + a(3) = 2 + 3 = 5 not yet in the sequence,
%e A328444 - so a(3) = 5.
%e A328444 For n = 5:
%e A328444 - the divisors of a(4) = 5 are all already in the sequence,
%e A328444 - 4 is the least divisor of a(3) + a(4) = 3 + 5 = 8 not yet in the sequence,
%e A328444 - so a(5) = 4.
%o A328444 (PARI) \\ See Links section.
%Y A328444 See A328443 for a similar sequence.
%Y A328444 Cf. A085947.
%K A328444 nonn
%O A328444 1,2
%A A328444 _Rémy Sigrist_, Oct 15 2019