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A096147 Prime denominators of the rational convergents to sqrt(3). 3
3, 11, 41, 571, 2131, 110771, 1542841, 15558008491, 808717138331, 1663476485027525263506023431291963826940251, 33648911495192637123958375850447995878147331088460770783226682531 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Next term is too large to include.

The next term has 79 digits. - Harvey P. Dale, Jul 06 2019

This is the prime subsequence of A002530. - Ray Chandler, Aug 01 2004

Primes p such that 3*p^2 - 2 is a square. - _ Vincenzo Librandi_, May 21 2013

LINKS

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

MATHEMATICA

Select[Denominator[Convergents[Sqrt[3], 300]], PrimeQ] (* Harvey P. Dale, Jul 06 2019 *)

PROG

(PARI) \Continued fraction rational approximation of numeric constants f. m=steps. cfracdenomprime(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(denom), print1(denom, ", ")); ) }

CROSSREFS

Cf. A002530, A079935.

Sequence in context: A018962 A102417 A342975 * A225431 A099489 A077830

Adjacent sequences:  A096144 A096145 A096146 * A096148 A096149 A096150

KEYWORD

nonn

AUTHOR

Cino Hilliard, Jul 24 2004

STATUS

approved

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Last modified April 21 17:04 EDT 2021. Contains 343156 sequences. (Running on oeis4.)