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A096146
Prime numerators of the rational convergents to sqrt(3).
2
2, 5, 7, 19, 71, 97, 3691, 191861, 138907099, 708158977, 26947261171
OFFSET
1,1
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
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
KEYWORD
nonn
AUTHOR
Cino Hilliard, Jul 24 2004
EXTENSIONS
Offset corrected by Amiram Eldar, Jul 11 2024
STATUS
approved