A111016 Starting with the fraction 1/1, prime denominators of fractions built according to the rule: add top and bottom to get the new bottom, add top and 10 times bottom to get the new top.

2, 13, 3457, 17797573, 105563930438375514795375041782813, 548910881501677043216804568782519749, 30150614379007816426425199846022140036752745857422145810701353231167111517347138427741849789

Offset

1,1

Comments

The next term (a(8)) has 924 digits. - Harvey P. Dale, Feb 06 2014

References

John Derbyshire, Prime Obsession, Joseph Henry Press, April 2004, p. 16.

Links

Table of n, a(n) for n=1..7.

Formula

Given a(0)=1, b(0)=1 then for i=1, 2, .. a(i)/b(i) = (a(i-1)+2*b(i-1)) /(a(i-1) + b(i-1)).

Mathematica

nxt[{t_, b_}]:={t+10b, t+b}; Select[Transpose[NestList[nxt, {1, 1}, 60]][[2]], PrimeQ] (* Harvey P. Dale, Feb 06 2014 *)

Prog

(PARI) primenum(n, k, typ) = \ k=mult, typ=1 num, 2 denom. output prime num or denom. { local(a, b, x, tmp, v); a=1; b=1; for(x=1, n, tmp=b; b=a+b; a=k*tmp+a; if(typ==1, v=a, v=b); if(isprime(v), print1(v", "); ) ); print(); print(a/b+.) }

Crossrefs

Also A015519(a(n)) is prime.

Sequence in context: A110820 A139519 A306206 * A176947 A280798 A118912

Adjacent sequences: A111013 A111014 A111015 * A111017 A111018 A111019

Keyword

easy,nonn

Author

Cino Hilliard, Oct 02 2005

Extensions

Edited by N. J. A. Sloane at the suggestion of Andrew S. Plewe, May 16 2007

One more term (a(7)) from Harvey P. Dale, Feb 06 2014

Status

approved