A242647 Sign of (the n-th continued fraction convergent to 2*Pi divided by the n-th convergent to Pi minus 2).

0, 1, -1, 1, -1, 1, -1, 0, 1, 0, 0, 0, 0, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 0, 0, 1, 0, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, 0, 0, 0, -1, 1, -1, 1, -1

Offset

1

Comments

Zeros appear in clusters (see A242857). Conjecture: Remove all zeros and the remaining terms will alternate signs.

References

Hans Havermann, Posting to Math Fun Mailing List, May 22 2014.

Links

Hans Havermann, Table of n, a(n) for n = 1..10000

Mathematica

Sign[Convergents[2*Pi, 200]/Convergents[Pi, 200]-2]

Crossrefs

Cf. A242857; Convergents to 2*Pi: A046955 (assuming offset 0)/A242859; Convergents to Pi: A002485/A002486 (both assuming offset -1).

Sequence in context: A182067 A196147 A097325 * A167393 A275606 A106549

Adjacent sequences: A242644 A242645 A242646 * A242648 A242649 A242650

Keyword

sign

Author

N. J. A. Sloane, May 23 2014

Status

approved