

A086397


Numerators of the rational convergents to sqrt(2) if both numerators and denominators are primes.


4




OFFSET

1,1


COMMENTS

Next term, if it exists, is bigger than 489 digits (the 1279th convergent to sqrt(2)).  Joshua Zucker, May 08 2006
Are the terms >= 7 the primes in A183064? Is this a subsequence of A088165?  R. J. Mathar, Aug 16 2019


LINKS

Table of n, a(n) for n=1..5.
Andrej Dujella, Mirela JukiÄ‡ Bokun, Ivan Soldo, A Pellian equation with primes and applications to D(1)quadruples, arXiv:1706.01959 [math.NT], 2017.


MATHEMATICA

For[n = 2, n < 1500, n++, a := Join[{1}, Table[2, {i, 2, n}]]; If[PrimeQ[Denominator[FromContinuedFraction[a]]], If[PrimeQ[Numerator[FromContinuedFraction[a]]], Print[Numerator[FromContinuedFraction[a]]]]]] (* Stefan Steinerberger, May 09 2006 *)


PROG

(PARI) cfracnumdenomprime(m, f) = { default(realprecision, 3000); cf = vector(m+10); x=f; for(n=0, m, i=floor(x); x=1/(xi); 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(numer)&&ispseudoprime(denom), print1(numer", "); numer2=numer; denom2=denom); ) default(realprecision, 28); }


CROSSREFS

Denominators are A118612.
Sequence in context: A181148 A179907 A080581 * A229941 A019018 A018993
Adjacent sequences: A086394 A086395 A086396 * A086398 A086399 A086400


KEYWORD

frac,more,nonn


AUTHOR

Cino Hilliard, Sep 06 2003


EXTENSIONS

More terms from Cino Hilliard, Jan 15 2005
Edited by N. J. A. Sloane, Aug 06 2009 at the suggestion of R. J. Mathar


STATUS

approved



