A069655 Maximum element in the simple continued fraction expansion for (1+1/n)^n.

2, 4, 3, 3, 20, 16, 11, 34, 18, 128, 56, 168, 39, 21, 162, 116, 37, 113, 72, 105, 73, 245, 244, 74, 159, 187, 253, 663, 101, 166, 34, 41, 87, 71, 46, 449, 181, 1874, 130, 215, 457, 317, 196, 256, 160, 107, 72, 147, 209, 114, 2632, 134, 252, 844, 1285, 341, 656

Offset

1,1

Comments

Limit_{n -> infinity} (1+1/n)^n = e.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Example

The simple continued fraction expansion of (1+1/10)^10 is [2, 1, 1, 2, 5, 1, 128, 1, 2, 12, 5, 3, 46, 1, 11, 7], hence a(10) = 128.

Mathematica

Table[ Max[ ContinuedFraction[ (1 + 1/n)^n]], {n, 1, 60}]

Crossrefs

Cf. A001113, A069887.

Sequence in context: A227418 A278447 A235590 * A353706 A004574 A333401

Adjacent sequences: A069652 A069653 A069654 * A069656 A069657 A069658

Keyword

easy,nonn

Author

Benoit Cloitre, May 09 2002

Status

approved