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A086397
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Numerators of the rational convergents to sqrt(2) if both numerators and denominators are primes.
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4
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OFFSET
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1,1
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COMMENTS
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Next term, if it exists, is bigger than 489 digits (the 1279th convergent to sqrt(2)). - Joshua Zucker, May 08 2006
Yes, the terms >= 7 are the primes in A183064 and are a subsequence of A088165. a(1)=3 is from the numerator of 3/2, but no other convergents > sqrt(2) can appear in this sequence because they all have even denominator. All terms >= 7 are lower principal convergents from A002315/A088165/A183064 - Martin Fuller, Apr 08 2023
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LINKS
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MATHEMATICA
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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 *)
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PROG
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(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); }
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CROSSREFS
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KEYWORD
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frac,more,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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