A375815 Lexicographically earliest sequence of positive integers such that for any n > 0, Sum_{k = 1..n} 1/(a(k)*a(n+1-k)) <= 1.

1, 2, 3, 3, 4, 4, 5, 5, 5, 5, 6, 6, 6, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 11, 10, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 12, 12, 13, 12, 13, 13, 13, 13, 13, 13, 14, 14, 14, 14, 14, 14, 14, 14, 14, 15, 14, 15, 15, 15

Offset

1,2

Comments

The variant with strict inequality (A375814) is finite; is this sequence infinite?

Links

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

Example

The first terms, alongside the corresponding sums, are:
  n   a(n)  Sum {k=1..n} 1/(a(k)*a(n+1-k))
  --  ----  ------------------------------
   1     1  1
   2     2  1
   3     3  11/12
   4     3  1
   5     4  17/18
   6     4  35/36
   7     5  167/180
   8     5  14/15
   9     5  77/80
  10     5  119/120
  11     6  77/80
  12     6  29/30
  13     6  443/450
  14     7  3007/3150
  15     7  6011/6300

Prog

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

Crossrefs

Cf. A375814, A375834.

Sequence in context: A341053 A126236 A198194 * A378760 A073047 A038567

Adjacent sequences: A375812 A375813 A375814 * A375816 A375817 A375818

Keyword

nonn

Author

Rémy Sigrist, Aug 30 2024

Status

approved