A106549 - OEIS

%I #9 Jul 05 2022 17:36:07

%S 0,-1,-1,-1,1,-1,-1,0,-1,-1,0,-1,1,0,-1,-1,0,0,-1,0,-1,-1,0,-1,1,0,-1,

%T 0,0,-1,-1,0,0,-1,0,-1,-1,0,0,-1,0,-1,0,0,-1,0,0,0,-1,0,-1,-1,0,-1,-1,

%U 0,-1,0,0,0,1,0,0,-1,0,-1,0,0,-1,-1,0,0,0,0,-1,-1,0,0,-1,0,0,-1,0,-1,1,0,-1

%N a(n) = -1 if 2*n-1 is a prime, 1 if 2*n-1 is a prime squared, or 0 otherwise.

%e a(1)=0 because 1 is neither a prime nor a prime squared;

%e a(2)=-1 because 3 is a prime;

%e a(5)=1 because 9 = 3^2 is a prime squared.

%t Table[Which[PrimeQ[2n+1],-1,PrimeQ[Sqrt[2n+1]],1,True,0],{n,0,120}] (* _Harvey P. Dale_, Jul 05 2022 *)

%K easy,sign

%O 1,1

%A _Giovanni Teofilatto_, May 09 2005

%E Definition changed to match the data by _N. J. A. Sloane_, Jul 05 2022 at the suggestion of _Harvey P. Dale_.