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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.
3
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
1,1
COMMENTS
Sum_{k = 2..300} 1/(a(k)*a(302-k)) > 1, hence the sequence is finite with 300 terms.
LINKS
EXAMPLE
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
PROG
(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]", "); ); }
CROSSREFS
Sequence in context: A085182 A211339 A087739 * A127763 A057367 A032634
KEYWORD
nonn,fini,full
AUTHOR
Rémy Sigrist, Aug 30 2024
STATUS
approved