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

1,1

Links

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

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

Extensions

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

Status

approved