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A225195 Primes p such that (p+nextprime(p))/2 is a perfect square. 4
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 *)

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 A255669

Adjacent sequences:  A225192 A225193 A225194 * A225196 A225197 A225198

KEYWORD

nonn

AUTHOR

Jayanta Basu, May 09 2013

STATUS

approved

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Last modified August 23 11:24 EDT 2019. Contains 326222 sequences. (Running on oeis4.)