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Search: id:A109845
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| A109845 |
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a(1) = 2; a(2n) = least common multiple of all previous terms + 1. a(2n+1) = least common multiple of all previous terms - 1. |
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+0
3
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| 2, 3, 5, 31, 929, 863971, 746445024869, 557180175152428473492031, 310449747582890872093779269721785644810947012929, 96379045774280656880008037888192772255684941220159788508646084243678677683026025975278640171971
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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For n > 2 a(2n) == 1 mod 10 and a(2n+1) == 9 mod 10. Conjecture : There are infinitely many primes in this sequence.
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FORMULA
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a(2n) = {product n = 1 to 2n-1, a(k) } +1. a(2n+1) = {product n = 1 to 2n, a(k) } -1
a(1)=2, a(2)=3 and a(n)=a(n-1)^2+(-1)^n*a(n-1)+(-1)^n for n>=3 - Walter A. Kehowski (wkehowski(AT)cox.net), Aug 15 2005
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MAPLE
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a[1]:=2: for n from 1 to 5 do a[2*n]:=1+lcm(seq(a[i], i=1..2*n-1)); a[2*n+1]:=-1+lcm(seq(a[j], j=1..2*n)): od: seq(a[n], n=1..10); (Deutsch)
a := proc(n) option remember; if n=1 then 2 elif n=2 then 3 else a(n-1)^2 + (-1)^n*a(n-1) + (-1)^n fi end: (Kehowski)
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CROSSREFS
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Sequence in context: A106308 A036797 A136611 this_sequence A041019 A041977 A089213
Adjacent sequences: A109842 A109843 A109844 this_sequence A109846 A109847 A109848
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KEYWORD
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easy,nonn
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AUTHOR
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Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Jul 06 2005
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EXTENSIONS
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More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Aug 06 2005
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