OFFSET
1,1
COMMENTS
1^2+2^2+3^2+4^2=30, 14^2+15^2+16^2+17^2+18^2=1230,..
If the average is allowed to be the sum of one or more consecutive squares, then there is one additional term 4 = 2^2. - Chai Wah Wu, Feb 03 2016
LINKS
Chai Wah Wu, Table of n, a(n) for n = 1..12411
MATHEMATICA
mx=600; mz=mx^2+(mx+1)^2; lst={}; Do[p=q^2; Do[p+=n^2; If[PrimeQ[p-1]&&PrimeQ[p+1], If[p>mz, Break[]]; AppendTo[lst, p]], {n, q+1, mx+1}], {q, 1, mx}]; Union@lst
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladimir Joseph Stephan Orlovsky, Mar 27 2010
EXTENSIONS
Definition clarified by Chai Wah Wu, Feb 03 2016
STATUS
approved