%I A115658
%S A115658 1,2,6,30030
%N A115658 a(n) is the smallest square-free a(n-1)-almost prime; a(1) = 1.
%C A115658 A subsequence of A002110. a(5) = prime(a(4))# = prime(30030)# = 350741# 
               [= A002110(30030)], a 152104-digit number. Compare with A007097 (primeth 
               recurrence): The current sequence is analogously the primorial(e)th 
               recurrence but grows faster even than A014221 (Ackermann function 
               A_3(n+1)). This suggests considering the analogues also for factorials, 
               hyperfactorials, etc., to see which may fit as OEIS entries.
%F A115658 a(n) = prime(a(n-1))# = prod(k=1, a(n-1), prime(k)) = A002110(a(n-1)) 
               for n >= 2; a(1) = 1.
%e A115658 a(4) = prime(a(3))# = prime(6)# = 13# = 2*3*5*7*11*13 = 30030 [= A002110(6)].
%Y A115658 Cf. A014221 (similar but not square-free), A002110 (primorials), A007097.
%Y A115658 Sequence in context: A162146 A055698 A121167 this_sequence A005607 A161563 
               A135408
%Y A115658 Adjacent sequences: A115655 A115656 A115657 this_sequence A115659 A115660 
               A115661
%K A115658 easy,nonn
%O A115658 1,2
%A A115658 Rick L. Shepherd (rshepherd2(AT)hotmail.com), Jan 28 2006