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A076692 Numbers n such that average of prime(n) and prime(n+1) is a perfect square. 1
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 (list; graph; refs; listen; history; text; internal format)
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 * A220586 A054300 A303360

Adjacent sequences:  A076689 A076690 A076691 * A076693 A076694 A076695

KEYWORD

easy,nonn

AUTHOR

Joseph L. Pe, Oct 25 2002

STATUS

approved

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Last modified February 25 19:39 EST 2021. Contains 341618 sequences. (Running on oeis4.)