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 A086397 Numerators of the rational convergents to sqrt(2) if both numerators and denominators are primes. 4
 3, 7, 41, 63018038201, 19175002942688032928599 (list; graph; refs; listen; history; text; internal format)
 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 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/(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(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

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Last modified October 26 11:29 EDT 2020. Contains 338027 sequences. (Running on oeis4.)