A225195 - OEIS

A225195

Primes p such that (p+nextprime(p))/2 is a perfect square.

3, 7, 61, 79, 139, 223, 317, 439, 619, 1087, 1669, 2593, 3593, 4093, 5179, 6079, 8461, 12541, 13687, 16633, 19037, 19597, 25261, 27211, 28219, 29581, 36857, 38011, 39199, 45361, 46649, 47521, 51977, 56167, 74527, 87013, 88801, 91807, 92413, 95479, 103681

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

Primes for which average of two consecutive primes is a perfect square.

LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..5000

EXAMPLE

61 is in the list since (61+67)/2=64=8^2.

MATHEMATICA

Select[Prime[Range[10000]], IntegerQ[Sqrt[(# + NextPrime[#])/2]] &]

Select[Partition[Prime[Range[10000]], 2, 1], IntegerQ[Sqrt[Mean[#]]]&][[All, 1]] (* Harvey P. Dale, Jan 12 2019 *)