A086383 Prime terms in the sequence of Pell numbers, A000129.

2, 5, 29, 5741, 33461, 44560482149, 1746860020068409, 68480406462161287469, 13558774610046711780701, 4125636888562548868221559797461449, 4760981394323203445293052612223893281

Offset

1,1

Comments

Previous Name: Primes found among the denominators of the continued fraction rational approximations to sqrt(2).

See A096650 for the indices. - Jon E. Schoenfield, Jan 25 2017

A056869 is essentially the same sequence. - Jianing Song, Jan 02 2019

Links

Harvey P. Dale, Table of n, a(n) for n = 1..23

J. L. Schiffman, Exploring the Fibonacci sequence of order two with CAS technology, Paper C027, Electronic Proceedings of the Twenty-fourth Annual International Conference on Technology in Collegiate Mathematics, Orlando, Florida, March 22-25, 2012. See p. 262. - N. J. A. Sloane, Mar 27 2014

Formula

a(n) = A000129(A096650(n)). - Jon E. Schoenfield, Jan 25 2017

a(n) = A056869(n-1), n > 1. - Jianing Song, Jan 02 2019

Example

a(1) = 2 = A000129(2), a(2) = 5 = A000129(3), a(3) = 29 = A000129(5), etc. - Zak Seidov, Oct 21 2013 [Corrected by Jianing Song, Jan 02 2019]

Mathematica

Select[Table[ChebyshevU[k, 3]-ChebyshevU[k-1, 3], {k, 0, 50}], PrimeQ] (* Ed Pegg Jr, May 10 2007 *)
Select[Denominator[Convergents[Sqrt[2], 150]], PrimeQ] (* Harvey P. Dale, Dec 19 2012 *)
Select[LinearRecurrence[{2, 1}, {0, 1}, 16], PrimeQ] (* Zak Seidov, Oct 21 2013 *)

Prog

(PARI) \\ Continued fraction rational approximation of numeric constants f. m=steps.
cfracdenomprime(m, f) = { default(realprecision, 3000); cf = vector(m+10); x=f; for(n=0, m, i=floor(x); x=1/(x-i); cf[n+1] = i; ); for(m1=0, m, r=cf[m1+1]; forstep(n=m1, 1, -1, r = 1/r; r+=cf[n]; ); numer=numerator(r); denom=denominator(r); if(ispseudoprime(denom), print1(denom, ", ")); ) }
(GAP) f:=[0, 1];; for n in [3..100] do f[n]:=2*f[n-1]+f[n-2]; od; a:=Filtered(f, IsPrime);; Print(a); # Muniru A Asiru, Jan 03 2019

Crossrefs

Cf. A000129, A056869, A096650.

Sequence in context: A073833 A229918 A179554 * A118612 A187628 A158866

Adjacent sequences: A086380 A086381 A086382 * A086384 A086385 A086386

Keyword

nonn

Author

Cino Hilliard, Sep 06 2003; corrected Jul 30 2004

Extensions

Name changed (to a Comments entry from Zak Seidov, Oct 21 2013) by Jon E. Schoenfield, Jan 26 2017

Status

approved