A115272
Primes p such that p + 2, 18*p^2 + 1, and 18*(p+2)^2 + 1 are all primes.
Original entry on oeis.org
29, 107, 431, 1487, 1607, 2141, 5501, 10139, 10271, 17579, 22481, 23057, 27479, 32369, 36341, 36929, 38447, 55931, 57527, 69827, 75539, 78539, 79691, 81047, 81971, 84179, 86027, 89561, 93761, 102059, 112571, 113147, 118799, 119687
Offset: 1
a(1)=29 because 31, 18*29^2 + 1 = 15139, and 18*31^2 + 1 = 17299 are all primes.
Cf.
A089001 (Numbers n such that 2*n^2 + 1 is prime),
A090612 (Numbers k such that the k-th prime is of the form 2*k^2+1),
A090698 (Primes of the form 2*n^2+1),
A113541 (Numbers n such that 18*n^2+1 is a multiple of 19).
A247965
a(n) is the smallest number k such that m*k^2+1 is prime for all m = 1 to n.
Original entry on oeis.org
1, 1, 6, 3240, 113730, 30473520, 3776600100, 16341921960, 3332396388090
Offset: 1
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
-
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:
-
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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