A375814 Lexicographically earliest sequence of positive integers such that for any n > 0, Sum_{k = 1..n} 1/(a(k)*a(n+1-k)) < 1.

2, 2, 2, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 6, 7, 8, 7, 8, 8, 7, 9, 8, 9, 9, 8, 10, 9, 9, 10, 10, 10, 10, 10, 10, 11, 10, 11, 11, 11, 12, 11, 11, 13, 11, 12, 12, 12, 13, 12, 12, 14, 12, 13, 14, 12, 14, 14, 13, 14, 13, 14, 15, 13, 15, 15, 13, 16, 14, 14, 16

Offset: 1

Author

Rémy Sigrist, Aug 30 2024

Keywords

• nonn
• fini
• full

Comments

Sum_{k = 2..300} 1/(a(k)*a(302-k)) > 1, hence the sequence is finite with 300 terms.

Examples

			The first terms, alongside the corresponding sums, are:
  n   a(n)  Sum_{k=1..n} 1/(a(k)*a(n+1-k))
  --  ----  ------------------------------
   1     2  1/4
   2     2  1/2
   3     2  3/4
   4     3  5/6
   5     3  11/12
   6     4  11/12
   7     4  17/18
   8     4  35/36
   9     5  44/45
  10     5  59/60
  11     5  239/240
  12     6  119/120
  13     6  79/80
  14     6  119/120
  15     7  991/1008
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..300

Crossrefs

Cf. A375815, A375834.

Programs

PARI

{ for (n = 1, #a = vector(72), if (n==1, a[n] = 2, x = sum(k = 2, n-1, 1/(a[k]*a[n+1-k])); if (x >= 1, break, a[n] = floor(2/(a[1]*(1-x)))+1;);); print1 (a[n]", ");); }