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

Author

Robert G. Wilson v, Jun 28 2004

Keywords

• nonn

Examples

			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.
		

Links

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

Crossrefs

Cf. A096693, A096695, A096705, A096707, 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[ # ] == 2 &]]

Extensions

a(45) from Robert Price, Nov 29 2023