A161002 Least prime of three consecutive primes (p1,p2,p3) such that p2-p1 and p3-p2 are both perfect squares.

9547, 12853, 22189, 22303, 27127, 29881, 32257, 40387, 42859, 46771, 46957, 47977, 57601, 60037, 60457, 71593, 72577, 73783, 77101, 84247, 88423, 89137, 90547, 93427, 97459, 97609, 97879, 112507, 115021, 118927, 126271, 127873, 131317

Offset: 1

Author

Ki Punches, Jun 01 2009

Keywords

• nonn

Comments

Sequence is probably infinite.

a(3859) = 11981443 is the first term in the sequence where neither of the prime gaps is 36.

Examples

			Consecutive primes (22189, 22193, 22229) have gaps (4, 36) so 22189 is in the sequence.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A138198.

Programs

Mathematica

Transpose[Select[Partition[Prime[Range[12300]],3,1],IntegerQ[Sqrt[#[[2]]- #[[1]]]]&&IntegerQ[Sqrt[#[[3]]-#[[2]]]]&]][[1]] (* Harvey P. Dale, Dec 21 2011 *)

Extensions

Edited by Ray Chandler, Jun 08 2009