%I #14 Jul 06 2019 14:22:36
%S 2,5,61,1831,1218127681,20911135539110754710115844300800001,
%T 205118220637830114524967273372102004176647676497164400621440204800001,
%U 6306868169346727750558231922137388394069771110701510995102537435289737085359877256031030165504001
%N Beginning with 2, a(n+1) is obtained as the least prime of the form a(n)*(m)*(m+1)*(m+2)...(m+k) +1 where a(n) was obtained as the least prime of the form a(n-1)*(r)*(r+1)*(r+2)...(m-1) +1 and so on.
%C Product [{a(k)-1}/{a(k-1)}]= 2*3*4*5*... for k = 2,3,4,... {(5-1)/2}*{(61-1)/5}*{(1831-1)/61}*... = {2}*{3*4}*{5*6}*....
%C Some of the larger entries may only correspond to probable primes.
%C The Magma Calculator (http://magma.maths.usyd.edu.au/calc/) confirms that all terms given above through a(8) are, in fact, prime. - _Jon E. Schoenfield_, Aug 24 2009
%e a(2) = 2*2 + 1 = 5, a(3) = 5*(3*4) + 1 = 61, a(4) = 61*(5*6) + 1 = 1831.
%K nonn
%O 1,1
%A _Amarnath Murthy_, Apr 14 2004
%E More terms from _Joshua Zucker_, Jul 24 2006