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A109904
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a(1) = 5. a(n+1) is the greatest prime of the form k*(a(n)-k) + 1. The least prime occurs for k = 1 and a(n+1) = a(n) in that case if no other value of k gives a prime then the sequence terminates.
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6
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OFFSET
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1,1
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COMMENTS
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For the first five terms k = floor(a(n)/2). k can take values from 1 to floor(a(n)/2). It is conjectured that at least one value of k, 2 <= k < floor(a(n)/2) gives a prime and the sequence is infinite.
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LINKS
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EXAMPLE
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a(2) = 2*3 + 1 = 7, a(3) = 3*4 + 1 = 13.
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PROG
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(PARI) { b(n)=forstep(k=n\2, 1, -1, if(isprime(k*(n-k)+1), return(k*(n-k)+1))); return(0) }
s=5; while(1, print1(s, ", "); s=b(s)) \\ Max Alekseyev, Oct 04 2005
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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