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 A096707 Balanced primes (A090403) of index 3. 7
 53, 607, 977, 1289, 2083, 2351, 4013, 5563, 8803, 10657, 11117, 12583, 14747, 16433, 18731, 22067, 22699, 28477, 32833, 39227, 39749, 41957, 44357, 46229, 46643, 50053, 50123, 51869, 53617, 54469, 56167, 63377, 63527, 66797, 74729, 75217 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS EXAMPLE 607 is a member because 607 = (601 + 607 + 613)/3 = (593 + 599 + 601 + 607 + 613 + 617 + 619)/7 = (401 + ... + 607 + ... + 823)/65. MATHEMATICA f[n_] := Block[{c = 0, k = 1, p = Prime[n], s = Plus @@ Table[ Prime[i], {i, n - 1, n + 1}]}, While[k != n - 1, If[s == (2k + 1)p, c++ ]; k++; s = s + Prime[n - k] + Prime[n + k]]; c]; Prime[ Select[ Range[2, 250], f[ # ] == 3 &]] CROSSREFS Cf. A096693, A096695, A096705, A096706, A096708, A096709. Sequence in context: A112749 A245589 A177141 * A219989 A027007 A142780 Adjacent sequences:  A096704 A096705 A096706 * A096708 A096709 A096710 KEYWORD nonn AUTHOR Robert G. Wilson v, Jun 28 2004 STATUS approved

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