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.

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.

Links

Table of n, a(n) for n=1..11.

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

Adjacent sequences: A101411 A101412 A101413 * A101415 A101416 A101417

Keyword

frac,nonn,base

Author

Cino Hilliard, Jan 16 2005

Status

approved