A115658 - OEIS

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A115658

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

1, 2, 6, 30030 (list; graph; refs; listen; history; internal format)

	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 analogues 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]`
	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# = 235711*13 = 30030 [= A002110(6)].`
	CROSSREFS	`Cf. A014221 (similar but not squarefree), A007097.` `Sequence in context: A162146 A055698 A121167 * A005607 A184391 A161563` `Adjacent sequences: A115655 A115656 A115657 * A115659 A115660 A115661`
	KEYWORD	`nonn`
	AUTHOR	`Rick L. Shepherd (rshepherd2(AT)hotmail.com), Jan 28 2006`

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Last modified February 16 20:06 EST 2012. Contains 205955 sequences.