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

Author

Randy L. Ekl, Dec 26 2016

Keywords

• nonn

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.

Examples

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

References

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

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).

Programs

PARI

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

Extensions

More terms from Jinyuan Wang, Mar 04 2020