This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A375834 #7 Aug 31 2024 08:32:17
%S A375834 2,2,2,3,3,3,3,3,4,3,4,4,4,4,4,4,4,4,4,4,4,4,4,5,4,5,4,5,4,5,4,5,5,5,
%T A375834 4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,5,5,5,
%U A375834 6,5,5,6,5,5,6,5,6,5,6,5,6,5,6,5,6,5,6
%N A375834 Lexicographically earliest sequence of positive integers such that for any n > 0, Sum_{k = 1..n} 1/(k*a(n+1-k)) < 1.
%C A375834 This sequence is unbounded.
%H A375834 Rémy Sigrist, <a href="/A375834/b375834.txt">Table of n, a(n) for n = 1..10000</a>
%e A375834 The first terms, alongside the corresponding sums, are:
%e A375834 n a(n) Sum {k=1..n} 1/(k*a(n+1-k))
%e A375834 -- ---- ---------------------------
%e A375834 1 2 1/2
%e A375834 2 2 3/4
%e A375834 3 2 11/12
%e A375834 4 3 7/8
%e A375834 5 3 107/120
%e A375834 6 3 331/360
%e A375834 7 3 299/315
%e A375834 8 3 4931/5040
%e A375834 9 4 4651/5040
%e A375834 10 3 4993/5040
%e A375834 11 4 26219/27720
%e A375834 12 4 155389/166320
%e A375834 13 4 201613/216216
%e A375834 14 4 288793/308880
%e A375834 15 4 2031847/2162160
%o A375834 (PARI) { for (n = 1, #a = vector(87), a[n] = floor(1/(1-sum(k = 2, n, 1/(k*a[n+1-k])))) + 1; print1 (a[n]", ");); }
%Y A375834 Cf. A374663, A375814, A375815.
%K A375834 nonn
%O A375834 1,1
%A A375834 _Rémy Sigrist_, Aug 31 2024