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EXAMPLE
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7, 13 & 17 have exactly two consecutive quadratic residues.
11, 41 & 53 have exactly three consecutive quadratic residues.
19, 23, 29, 31, 37, 47, 73, 89, 97, 149 & 193 have exactly four consecutive quadratic residues.
43, 59, 61, 109, 113, 139, 229, 313, 317, 337, 397 & 457 have exactly five consecutive quadratic residues.
67, 71, 79, 107, 137, 157, 163, 167, 173, 179, 181, 191, 199, 233, 239, 241, 257, 281, 349, 353, 373, 409, 431, 577, 601, 617, 641, 769, 797, 857, 881, 1049, 1373 & 2153 have exactly six consecutive quadratic residues.
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