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

Offset: 1

Author

Jayanta Basu, May 09 2013

Keywords

• nonn

Comments

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

Examples

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

Links

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

Crossrefs

Cf. A000040, A000290, A069495, A075190

Programs

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 *)

PARI

p=2;forprime(q=3,1e9,if(issquare((p+q)/2),print1(p", "));p=q) \\ Charles R Greathouse IV, May 09 2013