A184417 p^2 + (p+2)^2 - 1 where (p,p+2) is the n-th twin prime pair.

33, 73, 289, 649, 1801, 3529, 7201, 10369, 20809, 23329, 38089, 45001, 64801, 73729, 78409, 103969, 115201, 145801, 159049, 194689, 242209, 352801, 373249, 426889, 544969, 649801, 720001, 763849, 824329, 871201, 1312201, 1351369, 1371169, 1472329, 1555849, 2080801, 2130049, 2205001, 2255689, 2384929, 2654209

Offset: 1

Author

Robert Mohr, Feb 13 2011

Keywords

• nonn

Comments

This seems to have a disproportionately high probability of generating a prime number.

Examples

			a(1) = prime(1)^2 + (prime(1)+2)^2 - 1 =  3^2 +  (3+2)^2 - 1 =  33;
a(2) = prime(2)^2 + (prime(2)+2)^2 - 1 =  5^2 +  (5+2)^2 - 1 =  73;
a(3) = prime(3)^2 + (prime(3)+2)^2 - 1 = 11^2 + (11+2)^2 - 1 = 289.
		

Programs

Mathematica

Total/@(Select[Partition[Prime[Range[500]],2,1],#[[2]]-#[[1]]==2&]^2)-1  (* Harvey P. Dale, Feb 24 2011 *)

Formula

a(n) = A063533(n) - 1.