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 A193143 Primes which are the sum of 5 distinct positive squares in more than one way. 3
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS All terms from 103 onwards in A068229 are primes which are the sum of 5 distinct positive squares in more than one way. LINKS EXAMPLE 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. 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] CROSSREFS Cf. A068229, A085317, A193141, A193142. Sequence in context: A274518 A066131 A095639 * A098049 A055628 A139643 Adjacent sequences:  A193140 A193141 A193142 * A193144 A193145 A193146 KEYWORD nonn AUTHOR Vladimir Joseph Stephan Orlovsky, Jul 16 2011 STATUS approved

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Last modified July 23 20:42 EDT 2019. Contains 325264 sequences. (Running on oeis4.)