A034881 a(1) = 1; for n>1, a(n) = smallest integer > a(n-1) such that a(n)*a(i)+1 is prime for all 1 <= i <= n-1.

1, 2, 6, 18, 30, 270, 606, 123120, 888456, 23070450, 238550160, 8282903640, 72789145650, 15681266370000, 18216437241240

Offset: 1

Author

Erich Friedman

Keywords

• nonn

Comments

a(16) > 2*10^16.

a(n) exists for every n if Dickson's conjecture is true. - Charles R Greathouse IV, Nov 30 2012

Examples

			After a(1)=1, a(2)=2, a(3)=6, we want m, the smallest number >6 such that m+1, 2m+1 and 6m+1 are all prime: this is m = 18 = a(4).
		

Links

• Bill Taylor et al., Sets producing primes, sci.math (2003)

Crossrefs

Cf. A219761, A093483.

Programs

Mathematica

f[s_List] := Block[{k = s[[-1]] + 1, m = s}, While[ Union@ PrimeQ[k*m + 1] != {True}, k++]; Append[s, k]]; Nest[f, {1}, 10] (* Robert G. Wilson v, Dec 02 2012 *)

Extensions

a(9)-a(13) found by Phil Carmody.

a(14)-a(15) from Don Reble, Oct 15 2012

Edited by N. J. A. Sloane, Dec 01 2012