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

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

Offset

0,1

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

Table of n, a(n) for n=0..10.

Mathematica

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

Prog

(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, ", ")); ) }

Crossrefs

Cf. A002531, A082630, A086386.

Sequence in context: A106872 A071198 A041387 * A041583 A143915 A355597

Adjacent sequences: A096143 A096144 A096145 * A096147 A096148 A096149

Keyword

nonn

Author

Cino Hilliard, Jul 24 2004

Status

approved