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A086383 Primes found among the denominators of the continued fraction rational approximations to sqrt(2). 5
2, 5, 29, 5741, 33461, 44560482149, 1746860020068409, 68480406462161287469, 13558774610046711780701, 4125636888562548868221559797461449, 4760981394323203445293052612223893281 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Also, prime terms in the sequence of Pell numbers, A000129. - Zak Seidov, Oct 21 2013

REFERENCES

J. L. Schiffman, Exploring the Fibonacci sequence of order two with CAS technology, http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.392.6982&rep=rep1&type=pdf; no date. See p. 262. - N. J. A. Sloane, Mar 27 2014

LINKS

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

EXAMPLE

a(1) = 2 = A000129(3), a(2) = 5 = A000129(4), a(3) = 29 = A000129(6), etc. - Zak Seidov, Oct 21 2013

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, ", ")); ) }

CROSSREFS

Cf. A000129, A056869.

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

STATUS

approved

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Last modified August 20 18:07 EDT 2014. Contains 245801 sequences.