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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).

%I A093777 #23 Jul 13 2023 01:13:41
%S A093777 2,2,19,199,2089,99109,1960969,10129129,87726649,4549584049,
%T A093777 328034245549,20584643748679,666188861477149,31395465477725359,
%U A093777 894857713367947339,434392154438254391389,17934770256689308411399
%N 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).
%C A093777 Thanks in part to Dirichlet's theorem, a(n) exists for each n. - _Don Reble_, Oct 07 2006
%H A093777 Toshitaka Suzuki, <a href="/A093777/b093777.txt">Table of n, a(n) for n = 1..100</a>
%e A093777 a(1) = a(2) = 2 because they generate {2,3,7,43,13,...};
%e A093777 a(3) = 19 because it generates {19,2,3,5,571,271,...}, see A051312;
%e A093777 a(4) = 199 because it generates {199,2,3,5,7,23,881,...};
%e A093777 a(5) = 2089 because it generates {2089,2,3,5,7,11,269,...};
%e A093777 a(6) = 99109 because it generates {99109,2,3,5,7,11,13,2976243271,...};
%e A093777 a(7) = 1960969 because it generates {1960969,2,3,5,7,11,13,17,281,47,419,5539788476533581271,37,19,173,...}
%Y A093777 Cf. A093778, A093779, A093780, A000945, A051309-A051334, A051614-A051616, A056756.
%K A093777 nonn
%O A093777 1,1
%A A093777 _Labos Elemer_, May 03 2004
%E A093777 More terms from _Don Reble_, Oct 07 2006