A090685 -id:A090685 - cp's OEIS frontend

A188549 Numbers k such that 8*k^2+1 is a prime.

3, 12, 15, 18, 21, 33, 36, 48, 51, 66, 78, 81, 93, 102, 114, 120, 132, 150, 153, 162, 180, 183, 213, 225, 228, 231, 234, 237, 243, 246, 252, 279, 282, 285, 294, 303, 318, 324, 333, 375, 378, 381, 384, 393, 396, 399, 417, 432, 450, 459, 468, 480, 489, 495, 510

Offset: 1

Vincenzo Librandi, Apr 04 2011

Half of the even terms of A089001. - R. J. Mathar, Apr 09 2011

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A090685 (Primes of the form 8*n^2 + 1), A089001.

[n: n in [1..1800]|IsPrime(8*n^2 + 1)]; // Vincenzo Librandi, Apr 04 2011

Select[Range[600],PrimeQ[8#^2+1]&] (* Harvey P. Dale, Apr 11 2012 *)

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

Michel Lagneau, Sep 28 2014

Conjecture : the sequence is infinite.

a(10) > 15466500000000. a(11) > 107669100000000. - Hiroaki Yamanouchi, Oct 01 2014

			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

Cf. A002496, A090698, A002648, A137530, A090687, A201602, A090685, A156226.

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

a(7)-a(9) from Hiroaki Yamanouchi, Oct 01 2014

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A188549 Numbers k such that 8*k^2+1 is a prime.

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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.

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