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

Author

Harvey Dubner (harvey(AT)dubner.com)

Keywords

• nonn

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

Crossrefs

For the primes so generated see A087864.

Cf. A083771.

Programs

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 *)

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.

Extensions

Corrected and extended by Ray Chandler, Nov 06 2003

Further terms from Lei Zhou, Dec 08 2005