OFFSET
1,1
COMMENTS
"Does the sequence [above] contain every prime? Is the sequence infinite?" ... "The sequence of problem [above] is not even known to be infinite, though it almost surely contains every prime. We do not know whether anyone has attacked the problem computationally; perhaps you, the reader, would like to give it a try. The problem is due to M. Newman at the Australian Nation University." - Crandall and Pomerance
No more out-of-order primes up to 100 billion. - Charles R Greathouse IV, Apr 26 2010.
REFERENCES
R. Crandall and C. Pomerance, Prime Numbers: A Computational Perspective, Springer, NY, 2001; see p. 6.
EXAMPLE
a(3) is equal to 5 because a(1)*a(1)+1 = 2*2+1 = 5.
MATHEMATICA
a = {2, 3}; Do[l = Length[a]; a = Append[ a, Complement[ Union[Flatten[ Table[ Transpose[ FactorInteger[ a[[i]]*a[[j]] + 1]] [[1]], {i, 1, l}, {j, 1, i} ]]], a] [[1]]], {n, 3, 100} ]; a
CROSSREFS
KEYWORD
nonn
AUTHOR
Robert G. Wilson v, Sep 04 2001
EXTENSIONS
Comment and cross-reference from Charles R Greathouse IV, Apr 26 2010
STATUS
approved