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A084598
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a(1) = 2, a(2) = 3; for n >= 2, a(n+1) is smallest prime factor of (Product_{k = 1..n} a(k)) - 1.
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3
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2, 3, 5, 29, 11, 7, 13, 37, 32222189, 131, 136013303998782209, 31, 197, 19, 157, 17, 8609, 1831129, 35977, 508326079288931, 487, 10253, 1390043, 18122659735201507243, 25319167, 9512386441, 85577, 1031, 3650460767, 107
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Like the Euclid-Mullin sequence A000945, but subtracting rather than adding 1 to the product.
The first 4 terms are identical with A084599. It starts diverging at a(5) because the factorization of 2*3*5*29-1=869=11*79 gives A084598(5)=11 and A084599(5)=79. - Hugo Pfoertner (hugo(AT)pfoertner.org), Mar 31 2004
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LINKS
| Sean A. Irvine (sairvin(AT)xtra.co.nz) added terms 54 through 61, May 21 2006, giving Table of n, a(n) for n = 1..61
Dario Alpern, ECM
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EXAMPLE
| a(4)=29 since 2*3*5=30 and 29 is the smallest prime factor of 30-1
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CROSSREFS
| Cf. A000945, A005266, A084599.
Essentially the same as A005265.
Sequence in context: A041585 A042935 A102926 * A038962 A019400 A084599
Adjacent sequences: A084595 A084596 A084597 * A084599 A084600 A084601
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KEYWORD
| nonn
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AUTHOR
| Marc LeBrun (mlb(AT)well.com), May 31 2003
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EXTENSIONS
| More terms from Hugo Pfoertner (hugo(AT)pfoertner.org), May 31, 2003, using Dario Alpern's ECM.
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