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 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 (list; graph; refs; listen; history; text; internal format)
 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 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

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Last modified October 18 23:39 EDT 2019. Contains 328211 sequences. (Running on oeis4.)