

A069887


Number of terms in the simple continued fraction expansion for (1+1/n)^n.


4



1, 2, 5, 7, 7, 10, 14, 16, 24, 16, 20, 29, 39, 40, 42, 39, 46, 42, 44, 57, 59, 55, 66, 55, 57, 70, 68, 81, 86, 81, 91, 109, 106, 108, 119, 117, 123, 118, 124, 118, 120, 133, 142, 147, 164, 155, 159, 164, 167, 163, 177, 176, 168, 171, 198, 198, 201, 201, 205, 206, 227
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OFFSET

1,2


COMMENTS

lim_{n>infinity} (1+1/n)^n = e.
For any natural number N, limit_{n>infinity} (log(N)^(1/n) + 1/n)^n = e*log(N).  Alexander R. Povolotsky, Dec 06 2007


LINKS

G. C. Greubel, Table of n, a(n) for n = 1..1000


FORMULA

Asymptotically it seems that a(n)=C*n*log(n)) where C=0.84...is close to the constant described in A055573(n).


EXAMPLE

The simple continued fraction for (1+1/10)^10 is [2, 1, 1, 2, 5, 1, 128, 1, 2, 12, 5, 3, 46, 1, 11, 7] which contains 16 elements, hence a(10)=16.


MATHEMATICA

Table[Length[ContinuedFraction[(1+1/n)^n]], {n, 70}] (* Harvey P. Dale, Jun 12 2013 *)


CROSSREFS

Sequence in context: A199590 A096624 A145378 * A254340 A120303 A093413
Adjacent sequences: A069884 A069885 A069886 * A069888 A069889 A069890


KEYWORD

easy,nonn


AUTHOR

Benoit Cloitre, May 04 2002


STATUS

approved



