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A086788 Primes found among the denominators of the continued fraction rational approximations to Pi. 3
7, 113, 265381, 842468587426513207 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The next term is too large to include.

LINKS

Joerg Arndt, Table of n, a(n) for n = 1..10

Cino Hilliard, Continued fractions rational approximation of numeric constants. [needs login]

EXAMPLE

The first 5 rational approximations to Pi are 3/1, 22/7, 333/106, 355/113, 103993/33102 where 7, 113 are primes.

PROG

(PARI)

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, ", ")); ) }

(PARI)

default(realprecision, 10^5);

cf=contfrac(Pi);

n=0;

{ for(k=1, #cf,  \\ generate b-file

    pq = contfracpnqn( vector(k, j, cf[j]) );

    p = pq[1, 1];  q = pq[2, 1];

\\    if ( ispseudoprime(p), n+=1; print(n, " ", p) );  \\ A086785

    if ( ispseudoprime(q), n+=1; print(n, " ", q) );  \\ A086788

); }

/* Joerg Arndt, Apr 21 2013 */

CROSSREFS

Cf. A086791, A086785.

Sequence in context: A064330 A159552 A228929 * A199672 A240288 A220343

Adjacent sequences:  A086785 A086786 A086787 * A086789 A086790 A086791

KEYWORD

easy,nonn

AUTHOR

Cino Hilliard, Aug 04 2003; corrected Jul 30 2004

EXTENSIONS

Corrected offset, Joerg Arndt, Apr 21 2013

STATUS

approved

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Last modified October 20 20:24 EDT 2019. Contains 328273 sequences. (Running on oeis4.)