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Search: id:A086791
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| A086791 |
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Primes found among the numerators of the continued fraction rational approximations to e. |
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+0
2
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| 2, 3, 11, 19, 193, 49171, 1084483, 563501581931, 332993721039856822081, 3883282200001578119609988529770479452142437123001916048102414513139044082579
(list; graph; listen)
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OFFSET
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1,1
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LINKS
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Cino Hilliard, Continued fractions rational approximation of numeric constants.
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EXAMPLE
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The first 8 rational approximations to e are 2/1, 3/1, 8/3, 11/4, 19/7, 87/32, 106/39, 193/71. The numerators 2, 3, 11, 19, 193 are primes.
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PROGRAM
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(PARI) \Continued fraction rational approximation of numeric constants f. m=steps. cfracnumprime(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), print1(numer, ", ")); ) }
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CROSSREFS
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Cf. A086788.
Sequence in context: A051097 A076201 A129668 this_sequence A004687 A097895 A023182
Adjacent sequences: A086788 A086789 A086790 this_sequence A086792 A086793 A086794
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KEYWORD
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easy,nonn
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AUTHOR
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Cino Hilliard (hillcino368(AT)gmail.com), Aug 04 2003; corrected Jul 24 2004
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