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Primes p such that p^2 is an arithmetic average of 4 consecutive primes.
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%I #12 Oct 06 2021 07:47:38

%S 3,179,443,487,523,1237,1481,1571,1933,2293,2801,3307,3863,4073,4493,

%T 4787,4909,5399,5683,5693,6427,7433,7789,9067,9623,10607,10883,11437,

%U 11497,11579,12149,12263,12553,13337,13669,13841,14071,14723,14741,15569,15901,16381

%N Primes p such that p^2 is an arithmetic average of 4 consecutive primes.

%C 2*p is a term of A051395: 2*3 = A051395(1), 2*179 = A051395(10), 2*443 = A051395(22).

%e 3^2 = (5+7+11+13)/4, 179^2 = (32027+32029+32051+32057)/4.

%t Select[Sqrt[Mean[#]]&/@Partition[Prime[Range[147*10^5]],4,1],PrimeQ] (* _Harvey P. Dale_, Jul 27 2019 *)

%Y Cf. A051395.

%K nonn

%O 1,1

%A _Zak Seidov_, Oct 03 2012