

A216055


Numbers that are mean of four squares of distinct primes.


0



51, 63, 81, 87, 91, 93, 111, 117, 121, 123, 129, 133, 135, 139, 141, 147, 151, 153, 157, 165, 169, 171, 175, 177, 181, 183, 189, 193, 195, 199, 205, 207, 211, 213, 217, 219, 223, 231, 235, 237, 241, 247, 249, 253, 255, 259, 261, 265, 267, 271, 277, 279, 285
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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.


LINKS



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



STATUS

approved



