OFFSET
1,1
COMMENTS
Any four squares of odd primes have integer average.
First integers with two and three representations are 111 and 259:
111=(3^2+5^2+7^2+19^2)/4=(3^2+5^2+11^2+17^2)/4,
259=(5^2+7^2+11^2+29^2)/4=(5^2+11^2+19^2+23^2)/4=(7^2+13^2+17^2+23^2)/4.
First primes in this sequence are: 139, 151, 157, 181, 193, 199, 211, 223, 241, 271, 277, 307, 331, 337, 349.
First squares are:
{81, 121, 169, 289, 361, 441, 529, 625, 729, 841, 961, 1089, 1225}=
{9, 11, 13, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35}^2.
EXAMPLE
51=(3^2+5^2+7^2+11^2)/4, 63=(3^2+5^2+7^2+13^2)/4.
CROSSREFS
KEYWORD
nonn
AUTHOR
Zak Seidov, Aug 30 2012
STATUS
approved