A096706 Balanced primes (A090403) of index 2.

211, 263, 349, 397, 409, 439, 709, 751, 787, 827, 1153, 1187, 1259, 1487, 1523, 1531, 2281, 2287, 2347, 2621, 3037, 3109, 3313, 3329, 3539, 3673, 4357, 4397, 4493, 4951, 4969, 4987, 5189, 5303, 5347, 5857, 6323, 6337, 7583, 7907, 7933, 8429, 8713, 8821, 8951

Offset

1,1

Links

Robert Price, Table of n, a(n) for n = 1..753

Example

263 is a member because 263 = (257 + 263 + 269)/3
= (179 + 181 + 191 + 193 + 197 + 199 + 211 + 223 + 227 + 229 + 233 + 239 + 241 + 251 + 257 + 263 + 269 + 271 + 277 + 281 + 283 + 293 + 307 + 311 + 313 + 317 + 331 + 337 + 347 + 349 + 353)/31.

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[ # ] == 2 &]]

Crossrefs

Cf. A096693, A096695, A096705, A096707, A096708, A096709.

Sequence in context: A240918 A346948 A317394 * A001583 A308790 A137870

Adjacent sequences: A096703 A096704 A096705 * A096707 A096708 A096709

Keyword

nonn

Author

Robert G. Wilson v, Jun 28 2004

Extensions

a(45) from Robert Price, Nov 29 2023

Status

approved