A280135 Negative continued fraction of Pi (also called negative continued fraction expansion of Pi).

4, 2, 2, 2, 2, 2, 2, 17, 294, 3, 4, 5, 16, 2, 3, 4, 2, 4, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 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

Appears that these terms are related to continued fraction of Pi through simple transforms; original continued fraction terms X,1 -> negative continued fraction term X+2 (e.g., 15,1->17, and 292,1->294); other transforms are to be determined.

Examples

			Pi = 4 - (1 / (2 - (1 / (2 - (1 / ...))))).
		

References

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

Crossrefs

Cf. A001203 (continued fraction of Pi).

Cf. A133593 (exact continued fraction of Pi).

Cf. A280136 (negative continued fraction of e).

Programs

PARI

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