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 A164926 Least prime p such that x^2+x+p produces primes for x=0..n-1 and composite for x=n. 18
 2, 3, 107, 5, 347, 1607, 1277, 21557, 51867197, 11, 180078317, 1761702947, 8776320587, 27649987598537, 291598227841757, 17 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Other known values: a(16)=17 and a(40)=41 (which is generated by Euler's polynomial, A005846). There are no other terms less than 10^12. All of Euler's Lucky numbers, A014556, are in this sequence. Assuming the prime k-tuples conjecture, Mollin's theorem 2.1 shows this sequence is defined for n>0. a(21)=234505015943235329417 found by J. Waldvogel and Peter Leikauf. [Jens Kruse Andersen, Sep 09 2009] LINKS Table of n, a(n) for n=1..16. R. A. Goudsmit, Unusual Prime Number Sequences, Nature, Vol. 214 (June 10, 1967), page 1164. R. A. Mollin, Prime-Producing Quadratics, The American Mathematical Monthly, Vol. 104, No. 6 (Jun. - Jul., 1997), pp. 529-544. MATHEMATICA PrimeRun[p_Integer] := Module[{k=0}, While[PrimeQ[k^2+k+p], k++ ]; k]; nn=8; t=Table[0, {nn}]; cnt=0; p=1; While[cnt

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Last modified October 4 17:22 EDT 2023. Contains 365887 sequences. (Running on oeis4.)