A096146 - OEIS

%I #15 Jul 11 2024 02:08:08

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

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

%C Next term is too large to include.

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

%H Amiram Eldar, <a href="/A096146/b096146.txt">Table of n, a(n) for n = 1..18</a>

%t Select[Numerator[Convergents[Sqrt[3],200]],PrimeQ] (* _Harvey P. Dale_, Nov 08 2022 *)

%o (PARI) \\ Continued fraction rational approximation of numeric constants f. m=steps.

%o 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,", ")); ) }

%Y Cf. A002531, A082630, A086386, A096147.

%K nonn

%O 1,1

%A _Cino Hilliard_, Jul 24 2004

%E Offset corrected by _Amiram Eldar_, Jul 11 2024