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

1,1

Comments

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

a(11) > 25000.

Links

Table of n, a(n) for n=1..10.

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 *)

Crossrefs

Cf. A094007, A002486.

Sequence in context: A092329 A053548 A054119 * A274758 A266929 A242986

Adjacent sequences: A259487 A259488 A259489 * A259491 A259492 A259493

Keyword

nonn,more

Author

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

Status

approved