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Numbers n such that n+2*prime(n) is a perfect square.
+10
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14, 30, 67, 171, 246, 255, 315, 374, 455, 722, 822, 911, 963, 978, 1410, 1650, 1826, 2103, 2390, 2558, 2747, 3030, 3055, 3170, 6642, 8414, 8807, 8879, 10647, 10967, 11502, 11543, 11627, 11750, 12866, 13263, 13607, 15030, 16070, 16411, 16907
MATHEMATICA
Select[Range[17000], IntegerQ[Sqrt[#+2Prime[#]]]&] (* Harvey P. Dale, Aug 18 2011 *)
Numbers q such that q^2 = 2*prime(n) + n for some n.
+10
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10, 16, 27, 47, 58, 59, 67, 74, 83, 108, 116, 123, 127, 128, 158, 172, 182, 197, 212, 220, 229, 242, 243, 248, 374, 426, 437, 439, 485, 493, 506, 507, 509, 512, 538, 547, 555, 586, 608, 615, 625, 633, 654, 675, 701, 714, 728, 749, 754, 756, 759, 767, 816, 883
Prime numbers q such that q^2 = 2*prime(n) + n for some n.
+10
2
47, 59, 67, 83, 127, 197, 229, 439, 509, 547, 701, 883, 1447, 1451, 1493, 1693, 1697, 1787, 2141, 2371, 2447, 2551, 2609, 2791, 3001, 3299, 3347, 3739, 4703, 4729, 4787, 5471, 5569, 5801, 6247, 6449, 6907, 6947, 7283, 7907, 8069, 8233, 9013, 9151, 9547
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