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Search: id:A057131
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| A057131 |
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One less than six times product of first n primes of form 6k-1. |
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+0
2
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| 29, 329, 5609, 129029, 3741869, 153416669, 7210583489, 382160924969, 22547494573229, 1600872114699329, 132872385520044389, 11825642311283950709, 1194389873439679021709, 127799716458045655322969
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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a(n)=5 mod 6, so a(n) has at least one prime factor of form 6k-1, and this is not one of those included in the calculation of a(n); for example 5609 has 71 as a prime factor. Therefore there are an infinite number of prime numbers of form 6k-1 (and also of form 3k-1).
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FORMULA
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a(n) =(a(n-1)+1)*A007528(n)-1 =6*A057130(n)-1
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EXAMPLE
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a(3)=6*(5*11*17)-1=5609
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CROSSREFS
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Cf. A007528, A057130.
Sequence in context: A142380 A042632 A107966 this_sequence A125417 A022689 A077516
Adjacent sequences: A057128 A057129 A057130 this_sequence A057132 A057133 A057134
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KEYWORD
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nonn,easy
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AUTHOR
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Henry Bottomley (se16(AT)btinternet.com), Aug 11 2000
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EXTENSIONS
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More terms from Larry Reeves (larryr(AT)acm.org), Oct 06 2000
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