A375834 - OEIS

%I #7 Aug 31 2024 08:32:17

%S 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 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 6,5,5,6,5,5,6,5,6,5,6,5,6,5,6,5,6,5,6

%N Lexicographically earliest sequence of positive integers such that for any n > 0, Sum_{k = 1..n} 1/(k*a(n+1-k)) < 1.

%C This sequence is unbounded.

%H Rémy Sigrist, <a href="/A375834/b375834.txt">Table of n, a(n) for n = 1..10000</a>

%e The first terms, alongside the corresponding sums, are:

%e   n   a(n)  Sum {k=1..n} 1/(k*a(n+1-k))

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

%e    1     2  1/2

%e    2     2  3/4

%e    3     2  11/12

%e    4     3  7/8

%e    5     3  107/120

%e    6     3  331/360

%e    7     3  299/315

%e    8     3  4931/5040

%e    9     4  4651/5040

%e   10     3  4993/5040

%e   11     4  26219/27720

%e   12     4  155389/166320

%e   13     4  201613/216216

%e   14     4  288793/308880

%e   15     4  2031847/2162160

%o (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 Cf. A374663, A375814, A375815.

%K nonn

%O 1,1

%A _Rémy Sigrist_, Aug 31 2024