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Search: id:A101414
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| A101414 |
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Defiant primes of order 3. Primes p such that no prime numerator and denominator of the continued fraction rational approximation of the sqrt(p) exist for numerators less than 10^3 digits in length. |
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+0
1
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| 5, 17, 23, 37, 47, 53, 61, 79, 83, 97, 101
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Defiant primes of order k are also of order r where 0 < r < k.
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EXAMPLE
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The 8-th convergent of sqrt(5) is c = 51841/23184. c^2 = 5.00000000186..
but both numerator and denomonator are not prime.
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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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Sequence in context: A067377 A153504 A044438 this_sequence A105884 A019410 A133423
Adjacent sequences: A101411 A101412 A101413 this_sequence A101415 A101416 A101417
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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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