A216055 Numbers that are mean of four squares of distinct primes.

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

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

Table of n, a(n) for n=1..53.

Example

51=(3^2+5^2+7^2+11^2)/4, 63=(3^2+5^2+7^2+13^2)/4.

Crossrefs

Sequence in context: A045068 A050701 A206525 * A034819 A335346 A118147

Adjacent sequences: A216052 A216053 A216054 * A216056 A216057 A216058

Keyword

nonn

Author

Zak Seidov, Aug 30 2012

Status

approved