login
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.
0
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.
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
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