A085013 a(1) = 1; for n>1, a(n) = smallest prime > a(n-1) such that a(1)*...*a(n) + 2 is a prime.

1, 3, 5, 7, 13, 23, 29, 37, 43, 61, 73, 89, 137, 151, 167, 199, 269, 383, 397, 521, 619, 659, 739, 1217, 1307, 1613, 1741, 1847, 1873, 2039, 2473, 2521, 2531, 3011, 3391, 3637, 3793, 4201, 4751, 5039, 5879, 6299, 7307, 7829, 8243, 8933, 9781, 9829, 10069

Offset: 1

Author

Robert G. Wilson v, Jun 17 2003

Keywords

• nonn

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..200

Crossrefs

Cf. A083566.

Programs

Mathematica

a[1] = 1; a[n_] := a[n] = Block[{k = a[n - 1] + 2}, While[ !PrimeQ[k] || ! PrimeQ[ k * Times @@ Table[ a[i], {i, 1, n - 1}] + 2], k += 2]; k]; Table[ a[n], {n, 1, 49}]
nxt[{t_,a_}]:=Module[{p=NextPrime[a]},While[!PrimeQ[t*p+2],p= NextPrime[ p]];{t*p,p}]; NestList[nxt,{1,1},50][[All,2]] (* Harvey P. Dale, Jan 09 2022 *)