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A101414
Defiant primes of order 3. Primes p such that no prime numerator and denominator of the continued fraction rational approximation of sqrt(p) exist for numerators less than 10^3 digits in length.
0
5, 17, 23, 37, 47, 53, 61, 79, 83, 97, 101
OFFSET
1,1
COMMENTS
Defiant primes of order k are also of order r where 0 < r < k.
EXAMPLE
The 8th convergent of sqrt(5) is c = 51841/23184. c^2 = 5.00000000186... but both numerator and denominator are nonprime.
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); if(length(Str(numer))>999, break); ) }
CROSSREFS
Sequence in context: A337095 A153504 A044438 * A105884 A019410 A133423
KEYWORD
frac,nonn,base
AUTHOR
Cino Hilliard, Jan 16 2005
STATUS
approved