A259490 Numbers k such that the denominator of the n-th convergent of the continued fraction expansion of Pi is prime.

2, 4, 9, 33, 595, 1127, 2003, 3611, 4356, 6926

Offset: 1

Author

Jonathan Sondow and Robert G. Wilson v, Jun 28 2015

Keywords

• nonn
• more

Comments

These are the k such that A002486(k+1) is prime. - Michel Marcus, Jul 15 2015

a(11) > 25000.

Crossrefs

Cf. A094007, A002486.

Programs

Mathematica

$MaxExtraPrecision = 25000; lst = {}; cf = ContinuedFraction[Pi, 10000]; Do[ If[ PrimeQ[ Denominator[ FromContinuedFraction[ Take[ cf, n]] ]], AppendTo[lst, n]], {n, Length[cf]}]; lst
Position[Convergents[Pi,7000],?(PrimeQ[Denominator[#]]&)]//Flatten (* _Harvey P. Dale, Aug 12 2021 *)