A174604 a(1) = 1, then a(n) is the least integer > a(n-1) such that n is the maximum element in the continued fraction for 1/a(1) + 1/a(2) + ... + 1/a(n).

1, 2, 4, 13, 38, 51, 97, 124, 247, 295, 348, 398, 421, 494, 615, 881, 1105, 1252, 1616, 1634, 1637, 2222, 2410, 2478, 2583, 92598, 115781, 124161, 132776, 141565, 151072, 160466, 169593, 180127, 190982, 200776, 211896, 223261, 236300, 245322, 259018

Offset

1,2

Comments

Conjectures:

The sequence is well defined for any n.

Limit_{n->oo} a(n)^(1/n) = 1.

Links

Table of n, a(n) for n=1..41.

Example

The continued fraction for 1/a(1) + 1/a(2) = 1 + 1/2 is [1,2].
The c.f. for 1 + 1/2 + 1/3 is [1,1,5].
The c.f. for 1 + 1/2 + 1/4 is [1,1,3], whose maximum element is 3, hence a(3)=3.

Prog

(PARI) s=1; t=1; for(n=2, 50, s=s+1/t; t=t+1; while(abs(n-vecmax(contfrac(s+1/t)))>0, t++); print1(t, ", "))

Crossrefs

Sequence in context: A144924 A148252 A268698 * A148253 A148254 A163137

Adjacent sequences: A174601 A174602 A174603 * A174605 A174606 A174607

Keyword

nonn

Author

Benoit Cloitre, Mar 23 2010

Status

approved