A165234 Least prime p such that 2x^2 + p produces primes for x=0..n-1 and composite for x=n.

2, 17, 3, 1481, 5, 149, 569, 2081, 2339, 5939831, 11, 33164857769

Offset

1,1

Comments

Other known values: a(14)=272259344081 and a(29)=29. There are no other terms less than 10^12. The primes p = 3, 5, 11, and 29 produce p consecutive distinct primes because the imaginary quadratic field Q(sqrt(-2p)) has class number 2. Assuming the prime k-tuples conjecture, this sequence is defined for n>0.

References

Paulo Ribenboim, My Numbers, My Friends, Springer,2000, pp. 349-350.

Links

Table of n, a(n) for n=1..12.

R. A. Mollin, Prime-producing quadratics, Amer. Math. Monthly 104 (1997), 529-544.

Eric W. Weisstein, Prime-Generating Polynomial

Mathematica

PrimeRun[p_Integer] := Module[{k=0}, While[PrimeQ[2k^2+p], k++ ]; k]; nn=9; t=Table[0, {nn}]; cnt=0; p=1; While[cnt<nn, p=NextPrime[p]; n=PrimeRun[p]; If[n<=nn && t[[n]]==0, t[[n]]=p; cnt++ ]]; t

Crossrefs

Cf. A007641, A050265, A161008, A164926.

Sequence in context: A108883 A199295 A162623 * A155895 A293179 A144212

Adjacent sequences: A165231 A165232 A165233 * A165235 A165236 A165237

Keyword

hard,nonn,more

Author

T. D. Noe, Sep 09 2009

Status

approved