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
Indices of primes in this sequence: 1, 2, 4, 3, 5, 6, 7, 9, 10, 8, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, ..., . It appears that only the primes 7 and 19 are out of order in the first 1000. - Robert G. Wilson v, Apr 12 2006 [corrected by Sergey Pavlov, Apr 26 2017]
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 7 because a(1)*a(2)+1 = 2*3+1 = 7.
MATHEMATICA
a = {2, 3}; Do[len = Length@a; AppendTo[a, Complement[a, Union@ Flatten@ Table[ First /@ FactorInteger[a[[i]]*a[[j]] + 1], {i, len}, {j, i}]] [[1]]], {n, 3, 60}]; 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