A076692 - OEIS

%I #6 May 17 2017 09:13:10

%S 2,4,18,22,34,48,66,85,114,181,263,378,503,564,690,793,1058,1498,1617,

%T 1924,2163,2223,2788,2980,3076,3211,3908,4018,4127,4707,4821,4899,

%U 5318,5698,7351,8452,8600,8870,8928,9205,9907

%N Numbers n such that average of prime(n) and prime(n+1) is a perfect square.

%H Harvey P. Dale, <a href="/A076692/b076692.txt">Table of n, a(n) for n = 1..500</a>

%e The average of prime(4) and prime(5) is (7 + 11)/2 = 3^2, so 4 is a term of the sequence.

%t Select[Range[10^4], IntegerQ[Sqrt[(Prime[ # ] + Prime[ # + 1])/2]] &]

%t Position[Mean/@Partition[Prime[Range[10000]],2,1],_?(IntegerQ[ Sqrt[ #]]&)]//Flatten (* _Harvey P. Dale_, May 17 2017 *)

%K easy,nonn

%O 1,1

%A _Joseph L. Pe_, Oct 25 2002