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%I #23 May 01 2017 09:32:10
%S 2,3,7,5,11,13,17,23,29,19,31,37,41,43,47,53,59,61,67,71,73,79,83,89,
%T 97,101,103,107,109,113,127,131,137,139,149,151,157,163,167,173,179,
%U 181,191,193,197,199,211,223,227,229,233,239,241,251,257,263,269,271
%N 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.
%C "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
%C 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]
%C No more out-of-order primes up to 100 billion. - _Charles R Greathouse IV_, Apr 26 2010.
%D R. Crandall and C. Pomerance, Prime Numbers: A Computational Perspective, Springer, NY, 2001; see p. 6.
%e a(3) is equal to 7 because a(1)*a(2)+1 = 2*3+1 = 7.
%t 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
%Y Cf. A063884.
%K nonn
%O 1,1
%A _Robert G. Wilson v_, Sep 04 2001
%E Comment and cross-reference from _Charles R Greathouse IV_, Apr 26 2010
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