A101415 Amenable primes of order 3. Primes p such that the numerator and denominator of the continued fraction rational approximation of sqrt(p) are both prime and the numerator is less than 10^3 digits in length.

2, 3, 7, 13, 19, 29, 31, 41, 43, 59, 67, 71, 73, 89

Offset

1,1

Comments

Amenable primes of order k are also amenable primes of order k+1.

Links

Table of n, a(n) for n=1..14.

Example

13 is a term because 7/2 is a rational convergent of sqrt(13), the length of 7 is < 10^3, and 7 and 2 are primes. 11/3 is the only other convergent for sqrt(13) that has a numerator < 10^3 digits.

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: A100764 A076974 A051484 * A210393 A045331 A053613

Adjacent sequences: A101412 A101413 A101414 * A101416 A101417 A101418

Keyword

frac,nonn,base

Author

Cino Hilliard, Jan 16 2005

Status

approved