A280136 Negative continued fraction of e (or negative continued fraction expansion of e).

3, 4, 3, 2, 2, 2, 3, 8, 3, 2, 2, 2, 2, 2, 2, 2, 3, 12, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 16, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 20, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 24, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2

Offset

1,1

Comments

After the first term (3), a pattern of groups consisting, for m>=1, of the number 4m, followed by 3, then 4m-1 2's, then 3.

References

Leonard Eugene Dickson, History of the Theory of Numbers, page 379.

Links

Table of n, a(n) for n=1..86.

Example

e = 2.71828... = 3 - (1/(4 - (1/(3 - (1/(...))))).

Prog

(PARI)  \p10000; p=exp(1.0); for(i=1, 300, print(i, " ", ceil(p)); p=ceil(p)-p; p=1/p )

Crossrefs

Cf. A003417 (continued fraction of e).

Cf. A005131 (generalized continued fraction of e).

Cf. A133570 (exact continued fraction of e).

Cf. A228825 (delayed continued fraction of e).

Cf. A280135 (negative continued fraction of Pi).

Sequence in context: A225445 A167877 A308430 * A258451 A332412 A333229

Adjacent sequences: A280133 A280134 A280135 * A280137 A280138 A280139

Keyword

nonn

Author

Randy L. Ekl, Dec 26 2016

Extensions

More terms from Jinyuan Wang, Mar 04 2020

Status

approved