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%I #10 Feb 02 2017 00:11:50
%S 1,2,6,30030
%N a(n) is the smallest product of a(n-1) distinct primes; a(1) = 1.
%C 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 analogs also for factorials, hyperfactorials, etc., to see which may fit as OEIS entries.
%C This sequence has tetrational growth. a(4) has 5 decimal digits; a(5) has 152,104 decimal digits; a(6) has about 2.1292101 * 10^152097 decimal digits. - _Charles R Greathouse IV_, Dec 09 2011
%F 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 a(4) = prime(a(3))# = prime(6)# = 13# = 2*3*5*7*11*13 = 30030 [= A002110(6)].
%Y Cf. A014221 (similar but not squarefree), A007097.
%K nonn
%O 1,2
%A _Rick L. Shepherd_, Jan 28 2006
%E Name edited by _Charles R Greathouse IV_, Feb 02 2017
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