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Search: id:A101415
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| A101415 |
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Amenable primes of order 3. Primes p such that the numerator and denominator of the continued fraction rational approximation of the sqrt(p) are both prime and the numerator is less than 10^3 digits in length. |
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+0
1
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| 2, 3, 7, 13, 19, 29, 31, 41, 43, 59, 67, 71, 73, 89
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Amenable primes of order k are also amenable primes of order k+1.
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EXAMPLE
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13 is in the list because 7/2 is rational convergent of sqrt(13) and the length of 7 is < 10^3 and 7 and 2 are primes. 11/3 is the only other convergent for the sqrt(13) that has a numerator < 10^3 digits.
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PROGRAM
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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); if(length(Str(numer))>999, break); ) }
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CROSSREFS
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Adjacent sequences: A101412 A101413 A101414 this_sequence A101416 A101417 A101418
Sequence in context: A100764 A076974 A051484 this_sequence A045331 A053613 A013645
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KEYWORD
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frac,nonn
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AUTHOR
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Cino Hilliard (hillcino368(AT)gmail.com), Jan 16 2005
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