|
Search: id:A111009
|
|
|
| A111009 |
|
Starting a priori with the fraction 1/1, "the prime numerators of fractions built according to the rule: add top and bottom to get the new bottom, add top and 4 times bottom to get the new top." Also A046717(n) is prime. |
|
+0
1
|
|
| 5, 13, 41, 1093, 797161, 21523361, 926510094425921, 1716841910146256242328924544641, 3754733257489862401973357979128773, 6957596529882152968992225251835887181478451547013
(list; graph; listen)
|
|
|
OFFSET
|
1,1
|
|
|
COMMENT
|
Is there an infinity of primes in this sequence?
|
|
REFERENCES
|
Prime Obsession, John Derbyshire, 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)).
|
|
PROGRAM
|
(PARI) primenum(n, k, typ) = \ k=mult, typ=1 num, 2 denom. ouyput 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
|
Adjacent sequences: A111006 A111007 A111008 this_sequence A111010 A111011 A111012
Sequence in context: A046717 A080925 A085601 this_sequence A012172 A066873 A105262
|
|
KEYWORD
|
easy,nonn,uned
|
|
AUTHOR
|
Cino Hilliard (hillcino368(AT)gmail.com), Oct 02 2005
|
|
|
Search completed in 0.002 seconds
|
