A063884 a(1) = 2, a(2) = 3 and a(k+1) is the least prime not already chosen that divides some a(i)*a(j)+1, where 1<=i<=j<=k.

2, 3, 5, 7, 11, 13, 17, 23, 29, 19, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271

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.

Links

Table of n, a(n) for n=1..58.

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

Cf. A063904.

Sequence in context: A139054 A290959 A003309 * A316787 A165671 A162855

Adjacent sequences: A063881 A063882 A063883 * A063885 A063886 A063887

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