A039726 Recursive prime generating sequence.

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

Offset

1,1

References

H. Dubner, Recursive Prime Generating Sequences, Journal of Recreational Mathematics, 29(3) 170-175 1998 Baywood NY.

Links

Robert G. Wilson v, Table of n, a(n) for n = 1..350

Formula

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.

Mathematica

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 *)

Crossrefs

For the primes so generated see A087864.

Cf. A083771.

Sequence in context: A214197 A083771 A158069 * A340418 A115617 A003064

Adjacent sequences: A039723 A039724 A039725 * A039727 A039728 A039729

Keyword

nonn

Author

Harvey Dubner (harvey(AT)dubner.com)

Extensions

Corrected and extended by Ray Chandler, Nov 06 2003

Further terms from Lei Zhou, Dec 08 2005

Status

approved