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A039726
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Recursive prime generating sequence.
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9
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2, 3, 5, 7, 11, 19, 29, 37, 47, 67, 103, 179, 191, 223, 271, 293, 317, 577, 643, 673, 809, 863, 877, 1049, 1093, 1129, 1151, 1381, 1613, 1637, 2089, 2131, 2311, 2957, 3623, 3833, 4253, 4271, 4423, 4673, 5939, 7717, 8167, 9133, 9533, 9539, 9679, 11059, 11743, 11969, 14759, 15859, 15971, 16139, 17431, 17713, 17761, 19309, 19373, 20747, 20983, 23741, 25261, 25933
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OFFSET
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1,1
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REFERENCES
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H. Dubner, Recursive Prime Generating Sequences, Journal of Recreational Mathematics, 29(3) 170-175 1998 Baywood NY.
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LINKS
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FORMULA
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2*3*5*7*...*a(n) +1 is prime. a(n) is prime. a(n) > a(n-1) with a(n) being the smallest possible prime.
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MATHEMATICA
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k = 1; cp = 2; ct = 1; n[ct] = 2; While[ct < 64, k++; p = Prime[k]; cp1 = cp*p; If[PrimeQ[cp1 + 1], cp = cp1; ct++; n[ct] = p]]; Table[n[k], {k, 1, ct}] (Lei Zhou)
f[s_List] := Block[{p = Times @@ s, q = NextPrime@ s[[-1]]}, While[ !PrimeQ[p*q + 1], q = NextPrime@ q]; Append[s, q]]; Nest[f, {2}, 63] (* Robert G. Wilson v, Jul 20 2017 *)
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CROSSREFS
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For the primes so generated see A087864.
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KEYWORD
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nonn
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AUTHOR
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Harvey Dubner (harvey(AT)dubner.com)
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EXTENSIONS
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Further terms from Lei Zhou, Dec 08 2005
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STATUS
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approved
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