A224489 Smallest k such that k*2*p(n)^2-1 is prime.

1, 1, 3, 1, 1, 1, 1, 4, 4, 6, 4, 6, 1, 1, 9, 10, 1, 6, 4, 7, 1, 4, 3, 4, 3, 10, 4, 4, 1, 1, 1, 10, 1, 7, 6, 12, 1, 9, 6, 3, 1, 1, 6, 3, 1, 1, 1, 3, 3, 4, 4, 21, 4, 1, 3, 1, 6, 4, 1, 10, 3, 1, 15, 1, 3, 4, 9, 13, 10, 9, 1, 4, 1, 3, 1, 3, 12, 9, 6, 1, 1, 22, 4, 1

Offset: 1

Author

Pierre CAMI, Apr 08 2013

Keywords

• nonn

Examples

			1*2*2^2-1=7 is prime, p(1)=2 so a(1)=1.
1*2*3^2-1=17 is prime, p(2)=3 so a(2)=1.
1*2*5^2-1=49 is composite; 2*2*5^2-1=99 is composite; 3*2*5^2-1=149 is prime, p(3)=5 so a(3)=3.
		

Links

• Pierre CAMI, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A224490, A224491, A224492.

Programs

Magma

S:=[];
k:=1;
for n in [1..90] do
  while not IsPrime(k*2*NthPrime(n)^2-1) do
       k:=k+1;
  end while;
  Append(~S, k);
  k:=1;
end for;
S; // Bruno Berselli, Apr 18 2013

Mathematica

a[n_] := For[k = 1, True, k++, If[ PrimeQ[k*2*Prime[n]^2 - 1], Return[k]]]; Table[a[n], {n, 1, 100}] (* Jean-François Alcover, Apr 10 2013 *)