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

1,1

Comments

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

Links

Table of n, a(n) for n=1..41.

Formula

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

Example

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.

Mathematica

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

Crossrefs

Sequence in context: A015722 A103046 A063868 * A240884 A049012 A137187

Adjacent sequences: A184414 A184415 A184416 * A184418 A184419 A184420

Keyword

nonn

Author

Robert Mohr, Feb 13 2011

Status

approved