A101779 a(n) = least k such that all of k, 2k+1, 3k+2, ..., nk+n-1 are primes, or 0 if no such k is found.

2, 2, 3, 5, 5, 154769, 2894219, 2894219, 407874179, 214580145779, 9448481062019, 247236503934419, 2545206711847799, 18178612369988250179, 53792264108455702829

Offset: 1

Author

Jonathan Vos Post and Ray Chandler, Jan 13 2005

Keywords

• nonn

Comments

a(10) > 3691000000, Robert G. Wilson v, Mar 23 2007

By definition the same as A088651(n)-1 if k exists. It is conjectured k always exists. - a(10)-a(15) from Jens Kruse Andersen, May 02 2008

Crossrefs

Cf. A000040, A005384, A067256, A067257, A067258, A101767, A101768, A101769, A101770.

Cf. A088651.

Programs

Mathematica

f[1] = 2; f[n_] := f[n] = Block[{k = PrimePi@ f[n - 1], p, t = Table[i*p + (i - 1), {i, 2, n}]}, While[p = Prime@k; Union@PrimeQ@t != {True}, k++ ]; p]; Do[ Print[f@n // Timing], {n, 10}] (* Robert G. Wilson v, Mar 23 2007 *)

Extensions

a(10)-a(15) from Jens Kruse Andersen, May 02 2008