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
References
- John Derbyshire, Prime Obsession, Joseph Henry Press, April 2004, p. 16.
Crossrefs
Also A015519(a(n)) is prime.
Programs
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Mathematica
nxt[{t_,b_}]:={t+10b,t+b}; Select[Transpose[NestList[nxt,{1,1},60]][[2]], PrimeQ] (* Harvey P. Dale, Feb 06 2014 *) -
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+.) }
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)).
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
Comments