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Beginning with 2, a(n+1) is the least prime == 1 (mod (Sum_{i=1..n} a(i))).
2

%I #9 Nov 17 2018 22:14:15

%S 2,3,11,17,67,101,1609,1811,7243,43457,108643,488893,5214857,23466857,

%T 938674273,3872031377,29040235327,542084392769,65659972074139,

%U 3179324963589889,58420096205964211,1849969713188866681,76465414811806489481,1881049204370439641233,94052460218521982061649

%N Beginning with 2, a(n+1) is the least prime == 1 (mod (Sum_{i=1..n} a(i))).

%t s = t = 2; Print[t]; Do[k = 1; While[ !PrimeQ[k*t + 1], k++ ]; p = k*t + 1; Print[p]; t += p, {n, 2, 30}] (* _Ryan Propper_, Jul 29 2005 *)

%K nonn

%O 1,1

%A _Amarnath Murthy_, Dec 02 2003

%E More terms from _Ryan Propper_, Jul 29 2005

%E Further terms from _David Wasserman_, Nov 16 2005