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

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]

Name edited by Charles R Greathouse IV, Feb 02 2017

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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 analogs also for factorials, hyperfactorials, etc., to see which may fit as OEIS entries.

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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]

_Rick L. Shepherd (rshepherd2(AT)hotmail.com), _, Jan 28 2006

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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]

Cf. A014221 (similar but not squarefree), A002110 (primorials), A007097.

easy,nonn

nonn

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a(n) is the smallest square-free squarefree a(n-1)-almost prime; a(1) = 1.

Cf. A014221 (similar but not square-freesquarefree), A002110 (primorials), A007097.

easy,nonn,new

a(n) is the smallest square-free a(n-1)-almost prime; a(1) = 1.

1, 2, 6, 30030

1,2

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.

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

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

Cf. A014221 (similar but not square-free), A002110 (primorials), A007097.

easy,nonn

Rick L. Shepherd (rshepherd2(AT)hotmail.com), Jan 28 2006

approved