A096707 Balanced primes (A090403) of index 3.

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, 76597, 77023, 93997

Offset: 1

Author

Robert G. Wilson v, Jun 28 2004

Keywords

• nonn

Examples

			607 is a member because 607 = (601 + 607 + 613)/3 =
(593 + 599 + 601 + 607 + 613 + 617 + 619)/7 = (401 + ... + 607 + ... + 823)/65.
		

Links

• Robert Price, Table of n, a(n) for n = 1..85

Crossrefs

Cf. A096693, A096695, A096705, A096706, A096708, A096709.

Programs

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 &]]

Extensions

a(37)-a(39) from Robert Price, Nov 29 2023