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A247965
a(n) is the smallest number k such that m*k^2+1 is prime for all m = 1 to n.
0
1, 1, 6, 3240, 113730, 30473520, 3776600100, 16341921960, 3332396388090
OFFSET
1,3
COMMENTS
Conjecture : the sequence is infinite.
a(10) > 15466500000000. a(11) > 107669100000000. - Hiroaki Yamanouchi, Oct 01 2014
EXAMPLE
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;
... - Michel Marcus, Sep 29 2014
MAPLE
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:
PROG
(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
KEYWORD
nonn,hard,more
AUTHOR
Michel Lagneau, Sep 28 2014
EXTENSIONS
a(7)-a(9) from Hiroaki Yamanouchi, Oct 01 2014
STATUS
approved