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A247965
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a(n) is the smallest number k such that m*k^2+1 is prime for all m = 1 to n.
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0
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OFFSET
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1,3
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COMMENTS
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Conjecture : the sequence is infinite.
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LINKS
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EXAMPLE
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a(3)=6 because 6^2+1 = 37, 2*6^2+1 = 73 and 3*6^2+1 = 109 are prime numbers.
The resulting primes begin like this:
2;
2, 3;
37, 73, 109;
10497601, 20995201, 31492801, 41990401;
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MAPLE
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for n from 1 to 6 do:
ii:=0:
for k from 1 to 10^10 while(ii=0) do:
ind:=0:
for m from 1 to n do:
p:=m*k^2+1:
if type(p, prime) then
ind:=ind+1:
fi:
od:
if ind=n then
ii:=1:printf ( "%d %d \n", n, k):
fi:
od:
od:
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PROG
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(PARI)
a(n)=k=1; while(k, c=0; for(i=1, n, if(!ispseudoprime(i*k^2+1), c++; break)); if(!c, return(k)); if(c, k++))
n=1; while(n<10, print1(a(n), ", "); n++) \\ Derek Orr, Sep 28 2014
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CROSSREFS
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KEYWORD
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nonn,hard,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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