A076692 Numbers n such that average of prime(n) and prime(n+1) is a perfect square.

2, 4, 18, 22, 34, 48, 66, 85, 114, 181, 263, 378, 503, 564, 690, 793, 1058, 1498, 1617, 1924, 2163, 2223, 2788, 2980, 3076, 3211, 3908, 4018, 4127, 4707, 4821, 4899, 5318, 5698, 7351, 8452, 8600, 8870, 8928, 9205, 9907

Offset

1,1

Links

Harvey P. Dale, Table of n, a(n) for n = 1..500

Example

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

Mathematica

Select[Range[10^4], IntegerQ[Sqrt[(Prime[ # ] + Prime[ # + 1])/2]] &]
Position[Mean/@Partition[Prime[Range[10000]], 2, 1], _?(IntegerQ[ Sqrt[ #]]&)]//Flatten (* Harvey P. Dale, May 17 2017 *)

Crossrefs

Sequence in context: A143116 A304856 A115987 * A350629 A357998 A220586

Adjacent sequences: A076689 A076690 A076691 * A076693 A076694 A076695

Keyword

easy,nonn

Author

Joseph L. Pe, Oct 25 2002

Status

approved