A376244 - OEIS

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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.

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

Is this sequence infinite?

LINKS

Table of n, a(n) for n=1..30.

Rémy Sigrist, PARI program

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

Adjacent sequences: A376241 A376242 A376243 * A376245 A376246 A376247

KEYWORD

nonn,more

AUTHOR

Rémy Sigrist and N. J. A. Sloane, Sep 16 2024

STATUS

approved