A224609 Smallest j such that 2*j*prime(n)^3-1 is prime.

2, 1, 2, 7, 2, 7, 8, 6, 8, 5, 1, 3, 11, 1, 9, 3, 5, 1, 3, 15, 7, 3, 8, 8, 12, 2, 15, 3, 10, 2, 3, 12, 12, 1, 6, 6, 9, 3, 5, 2, 5, 1, 5, 10, 57, 1, 21, 1, 15, 9, 2, 3, 1, 5, 5, 3, 15, 6, 7, 5, 25, 6, 12, 11, 6, 5, 1, 9, 2, 19, 5, 9, 27, 1, 3, 11, 3, 15, 2, 6, 21

Offset: 1

Author

Pierre CAMI, Apr 12 2013

Keywords

• nonn

Comments

We are searching smallest j such that j*prime(n)*2*p(n)^2-1 is prime, for A224489 it is smallest k such that k*2*prime(n)^2-1 is prime, so here we replace smallest k by smallest j*prime(n).

Examples

			1*2*2^3-1= 15 is composite; 2*2*2^3-1= 31 is prime, so a(1)=2 as p(1)=2.
1*2*3^3-1=53 is prime, so a(2)=1 as p(2)=3.
1*2*5^3-1=249 is composite; 2*2*5^3=499 is prime, so a(3)=2 as p(3)=5.
		

Links

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

Crossrefs

Cf. A224489.

Programs

Magma

S:=[];
j:=1;
for n in [1..100] do
  while not IsPrime(2*j*NthPrime(n)^3-1) do
       j:=j+1;
  end while;
  Append(~S, j);
  j:=1;
end for;
S; // Bruno Berselli, Apr 18 2013

Mathematica

jmax = 10^5 (* sufficient up to 10^5 terms *); a[n_] := For[j = 1, j <= jmax, j++, p = Prime[n]; If[PrimeQ[j*2*p^3 - 1], Return[j]]]; Table[a[n], {n, 1, 100}] (* Jean-François Alcover, Apr 18 2013 *)

PARI

a(n)=my(P=2*prime(n)^3,j);while(!isprime(j++*P-1),);j \\ Charles R Greathouse IV, Apr 18 2013

Formula

a(n) = A053989(2p^3) where p is the n-th prime. - Charles R Greathouse IV, Apr 18 2013