A083566 a(1) = 1; for n>1, a(n) = smallest odd number > a(n-1) such that a(1)*...*a(n) + 2 is a prime.

1, 3, 5, 7, 9, 15, 19, 25, 27, 53, 57, 65, 71, 87, 101, 151, 195, 247, 253, 255, 277, 289, 291, 301, 321, 355, 361, 443, 455, 461, 491, 531, 533, 541, 599, 603, 619, 635, 647, 667, 805, 817, 871, 1003, 1011, 1179, 1205, 1223, 1327, 1357, 1531, 1551, 1603, 1619

Offset: 1

Author

Amarnath Murthy and Meenakshi Srikanth (menakan_s(AT)yahoo.com), Jun 13 2003

Keywords

• nonn

Links

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

Crossrefs

Cf. A084723, A084724, A084725, A085013.

Programs

Mathematica

a[1] = 1; a[n_] := a[n] = Block[{k = a[n - 1] + 2}, While[ !PrimeQ[k*Times @@ Table[a[i], {i, 1, n - 1}] + 2], k += 2]; k]; Table[ a[n], {n, 1, 54}]
nxt[{pr_,a_}]:=Module[{k=a+2},While[!PrimeQ[pr k+2],k=k+2];{pr k,k}]; NestList[nxt,{1,1},60][[;;,2]] (* Harvey P. Dale, Jul 10 2023 *)

Extensions

Edited and extended by Robert G. Wilson v, Jun 17 2003

Edited by N. J. A. Sloane, Nov 01 2008 at the suggestion of R. J. Mathar