cp's OEIS Frontend

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.

%I A111016 #14 Sep 24 2018 16:53:14
%S A111016 2,13,3457,17797573,105563930438375514795375041782813,
%T A111016 548910881501677043216804568782519749,
%U A111016 30150614379007816426425199846022140036752745857422145810701353231167111517347138427741849789
%N 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.
%C A111016 The next term (a(8)) has 924 digits. - _Harvey P. Dale_, Feb 06 2014
%D A111016 John Derbyshire, Prime Obsession, Joseph Henry Press, April 2004, p. 16.
%F A111016 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)).
%t A111016 nxt[{t_,b_}]:={t+10b,t+b}; Select[Transpose[NestList[nxt,{1,1},60]][[2]], PrimeQ] (* _Harvey P. Dale_, Feb 06 2014 *)
%o A111016 (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+.) }
%Y A111016 Also A015519(a(n)) is prime.
%K A111016 easy,nonn
%O A111016 1,1
%A A111016 _Cino Hilliard_, Oct 02 2005
%E A111016 Edited by _N. J. A. Sloane_ at the suggestion of _Andrew S. Plewe_, May 16 2007
%E A111016 One more term (a(7)) from _Harvey P. Dale_, Feb 06 2014