A091457 Greatest numerator of the remainder in a reciprocal expansion of 1.

1, 1, 1, 5, 59, 4951, 9770455, 31950134954551

Offset

1,4

Comments

Conjecture: in the "extremal" expansion x_i = A000058(i) for i=1..n-3.

Links

Table of n, a(n) for n=1..8.

Formula

Let 1 = 1/x_1 + ... + 1/x_{n-1} + p/q, where 1/x_1>=...>=1/x_{n-1}>=p/q and (p, q)=1. a(n) = maximal p over all such expansions. Corresponded denominators sequence is A091458.

Example

a(7) = 9770455 because 1 = 1/2 + 1/3 + 1/7 + 1/43 + 1/5413 + 1/5419 + 9770455/52975482882 and there is no expansion with larger numerator of the remainder.

Crossrefs

Cf. A091458, A000058.

Sequence in context: A120608 A143766 A132549 * A289724 A100906 A126275

Adjacent sequences: A091454 A091455 A091456 * A091458 A091459 A091460

Keyword

frac,hard,nonn,more

Author

Max Alekseyev, Jan 11 2004

Status

approved