A093777 a(n) is the smallest prime which, if used to start a Euclid-Mullin sequence (like A000945), the resulting sequence contains the n consecutive primes 2, 3, ..., prime(n).

2, 2, 19, 199, 2089, 99109, 1960969, 10129129, 87726649, 4549584049, 328034245549, 20584643748679, 666188861477149, 31395465477725359, 894857713367947339, 434392154438254391389, 17934770256689308411399

Offset: 1

Author

Labos Elemer, May 03 2004

Keywords

• nonn

Comments

Thanks in part to Dirichlet's theorem, a(n) exists for each n. - Don Reble, Oct 07 2006

Examples

			a(1) = a(2) = 2 because they generate {2,3,7,43,13,...};
a(3) = 19 because it generates {19,2,3,5,571,271,...}, see A051312;
a(4) = 199 because it generates {199,2,3,5,7,23,881,...};
a(5) = 2089 because it generates {2089,2,3,5,7,11,269,...};
a(6) = 99109 because it generates {99109,2,3,5,7,11,13,2976243271,...};
a(7) = 1960969 because it generates {1960969,2,3,5,7,11,13,17,281,47,419,5539788476533581271,37,19,173,...}
		

Links

• Toshitaka Suzuki, Table of n, a(n) for n = 1..100

Crossrefs

Cf. A093778, A093779, A093780, A000945, A051309-A051334, A051614-A051616, A056756.

Extensions

More terms from Don Reble, Oct 07 2006