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

1,1

Comments

Sequence is probably infinite.

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

Links

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

Example

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

Mathematica

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

Crossrefs

Cf. A138198.

Sequence in context: A202613 A236161 A252512 * A134117 A353088 A232189

Adjacent sequences: A160999 A161000 A161001 * A161003 A161004 A161005

Keyword

nonn

Author

Ki Punches, Jun 01 2009

Extensions

Edited by Ray Chandler, Jun 08 2009

Status

approved