A115658 a(n) is the smallest product of a(n-1) distinct primes; a(1) = 1.

1, 2, 6, 30030

Offset

1,2

Comments

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.

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

Links

Table of n, a(n) for n=1..4.

Formula

a(n) = prime(a(n-1))# = prod(k=1, a(n-1), prime(k)) = A002110(a(n-1)) for n >= 2; a(1) = 1.

Example

a(4) = prime(a(3))# = prime(6)# = 13# = 2*3*5*7*11*13 = 30030 [= A002110(6)].

Crossrefs

Cf. A014221 (similar but not squarefree), A007097.

Sequence in context: A231545 A055698 A121167 * A337096 A005607 A184391

Adjacent sequences: A115655 A115656 A115657 * A115659 A115660 A115661

Keyword

nonn

Author

Rick L. Shepherd, Jan 28 2006

Extensions

Name edited by Charles R Greathouse IV, Feb 02 2017

Status

approved