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A376244
Lexicographically earliest sequence of positive integers a(1), a(2), ... with the property that the lexicographically earliest sequence of positive integers b(1), b(2), ... such that for any n > 0, S(n) = Sum_{k = 1..n} 1 / (a(k)*b(k)) < 1, also implies that S(n) is never of the form (e_n - 1) / e_n for some integer e_n.
4
3, 4, 5, 4, 7, 3, 9, 1, 11, 4, 13, 7, 9, 19, 10, 2, 23, 25, 29, 27, 53, 1, 17, 7, 2, 2, 15, 67, 22, 37
OFFSET
1,1
COMMENTS
Is this sequence infinite?
EXAMPLE
The initial terms are:
n a(n) b(n) S(n)
- ---- ------ ---------------------------
1 3 1 1/3
2 4 1 7/12
3 5 1 47/60
4 4 2 109/120
5 7 2 823/840
6 3 17 4757/4760
7 9 177 7582661/7582680
8 1 399089 3026164178509/3026164178520
PROG
(PARI) \\ See Links section.
CROSSREFS
Cf. A374663, A376062, A376184, A376245 (corresponding b's), A376246-A376247 (numerator and denominator of corresponding S(n)).
Sequence in context: A232702 A325272 A178698 * A225072 A262906 A243607
KEYWORD
nonn,more
AUTHOR
STATUS
approved