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%I #8 Nov 29 2023 16:38:03
%S 211,263,349,397,409,439,709,751,787,827,1153,1187,1259,1487,1523,
%T 1531,2281,2287,2347,2621,3037,3109,3313,3329,3539,3673,4357,4397,
%U 4493,4951,4969,4987,5189,5303,5347,5857,6323,6337,7583,7907,7933,8429,8713,8821,8951
%N Balanced primes (A090403) of index 2.
%H Robert Price, <a href="/A096706/b096706.txt">Table of n, a(n) for n = 1..753</a>
%e 263 is a member because 263 = (257 + 263 + 269)/3
%e = (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.
%t 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 &]]
%Y Cf. A096693, A096695, A096705, A096707, A096708, A096709.
%K nonn
%O 1,1
%A _Robert G. Wilson v_, Jun 28 2004
%E a(45) from _Robert Price_, Nov 29 2023
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