A193143 Primes which are the sum of 5 distinct positive squares in more than one way.

103, 127, 139, 151, 163, 167, 179, 191, 199, 211, 223, 227, 229, 239, 241, 251, 263, 271, 277, 281, 283, 307, 311, 313, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Jul 16 2011

Keywords

• nonn

Comments

All terms from 103 onwards in A068229 are primes which are the sum of 5 distinct positive squares in more than one way.

Examples

			103 = 1^2 + 2^2 + 3^2 + 5^2 + 8^2 = 2^2 + 3^2 + 4^2 + 5^2 + 7^2.
127 = 1^2 + 2^2 + 3^2 + 7^2 + 8^2 = 1^2 + 4^2 + 5^2 + 6^2 + 7^2 = 1^2 + 2^2 + 4^2 + 5^2 + 9^2.
		

Crossrefs

Cf. A068229, A085317, A193141, A193142.

Programs

Mathematica

sum5sqP = {}; Do[Do[Do[Do[Do[p = a^2 + b^2 + c^2 + d^2 + e^2; If[PrimeQ[p], AppendTo[sum5sqP, p]], {e, d - 1, 1, -1}], {d, c - 1, 1, -1}], {c, b - 1, 1, -1}], {b, a - 1, 1, -1}], {a, 6, 30}]; a = Take[Sort[sum5sqP], 1000]; a = Select[Table[If[a[[n]] == a[[n - 1]] && a[[n]] != a[[n - 2]], a[[n]], ""], {n, 3, Length[a]}], IntegerQ]