A375834 Lexicographically earliest sequence of positive integers such that for any n > 0, Sum_{k = 1..n} 1/(k*a(n+1-k)) < 1.

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, 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, 6, 5, 5, 6, 5, 5, 6, 5, 6, 5, 6, 5, 6, 5, 6, 5, 6, 5, 6

Offset: 1

Author

Rémy Sigrist, Aug 31 2024

Keywords

• nonn

Comments

This sequence is unbounded.

Examples

			The first terms, alongside the corresponding sums, are:
  n   a(n)  Sum {k=1..n} 1/(k*a(n+1-k))
  --  ----  ---------------------------
   1     2  1/2
   2     2  3/4
   3     2  11/12
   4     3  7/8
   5     3  107/120
   6     3  331/360
   7     3  299/315
   8     3  4931/5040
   9     4  4651/5040
  10     3  4993/5040
  11     4  26219/27720
  12     4  155389/166320
  13     4  201613/216216
  14     4  288793/308880
  15     4  2031847/2162160
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A374663, A375814, A375815.

Programs

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]", ");); }