A096146 Prime numerators of the rational convergents to sqrt(3).

2, 5, 7, 19, 71, 97, 3691, 191861, 138907099, 708158977, 26947261171

Offset: 1

Author

Cino Hilliard, Jul 24 2004

Keywords

• nonn

Comments

Next term is too large to include.

This is the prime subsequence of A002531. See also A086386 for numerators where both numerator and denominator are primes. - Ray Chandler, Aug 01 2004

Links

• Amiram Eldar, Table of n, a(n) for n = 1..18

Crossrefs

Cf. A002531, A082630, A086386, A096147.

Programs

Mathematica

Select[Numerator[Convergents[Sqrt[3],200]],PrimeQ] (* Harvey P. Dale, Nov 08 2022 *)

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,", ")); ) }

Extensions

Offset corrected by Amiram Eldar, Jul 11 2024