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

1,1

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 *)

Prog

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

Crossrefs

Cf. A000040, A000290, A069495, A075190

Sequence in context: A164895 A046859 A242380 * A084289 A183174 A329966

Adjacent sequences: A225192 A225193 A225194 * A225196 A225197 A225198

Keyword

nonn

Author

Jayanta Basu, May 09 2013

Status

approved