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A161002 Least prime of three consecutive primes (p1,p2,p3) such that p2-p1 and p3-p2 are both perfect squares. 3

%I

%S 9547,12853,22189,22303,27127,29881,32257,40387,42859,46771,46957,

%T 47977,57601,60037,60457,71593,72577,73783,77101,84247,88423,89137,

%U 90547,93427,97459,97609,97879,112507,115021,118927,126271,127873,131317

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

%C Sequence is probably infinite.

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

%H Harvey P. Dale, <a href="/A161002/b161002.txt">Table of n, a(n) for n = 1..1000</a>

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

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

%Y Cf. A138198.

%K nonn

%O 1,1

%A _Ki Punches_, Jun 01 2009

%E Edited by _Ray Chandler_, Jun 08 2009

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Last modified June 6 18:59 EDT 2020. Contains 334832 sequences. (Running on oeis4.)