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%I #2 Mar 30 2012 17:31:04
%S 2,5,211,53,157,173,304517
%N Least balanced prime (A090403) of index n (A096693).
%e a(1) = 5 because 5 = (3 + 5 + 7)/3.
%e a(2) = 211 because 211 = (199 + 211 + 223)/3
%e = (179 + 181 + 191 + 193 + 197 + 199 + 211 + 223 + 227 + 229 + 233 + 239 + 241)/13.
%e a(3) = 53 because 53 = (47 + 53 + 59)/3 = (41 + 43 + 47 + 53 + 59 + 61 + 67)/7
%e = (31 + 37 + 41 + 43 + 47 + 53 + 59 + 61 + 67 + 71 + 73)/11.
%e a(4) = 157 because 157 = (151 + 157 + 163)/3 = (139 + 149 + 151 + 157 + 163 + 167 + 173)/7
%e = (131 + 137 + 139 + 149 + 151 + 157 + 163 + 167 + 173 + 179 + 181)/11
%e = (97 + 101 + 103 + 107 + 109 + 113 + 127 + 131 + 137 + 139 + 149 + 151 + 157 + 163 + 167 + 173 + 179 + 181 + 191 + 193 + 197 + 199 + 211 + 223 + 227)/25.
%e a(5) = 173 because 173 = (167 + 173 + 179)/3 = (157 + 163 + 167 + 173 + 179 + 181 + 191)/7
%e = (131 + 137 + 139 + 149 + 151 + 157 + 163 + 167 + 173 + 179 + 181 + 191 + 193 + 197 + 199 + 211 + 223)/17
%e = (109 + 113 + 127 + 131 + 137 + 139 + 149 + 151 + 157 + 163 + 167 + 173 + 179 + 181 + 191 + 193 + 197 + 199 + 211 + 223 + 227 + 229 + 233)/23
%e = (107 + 109 + 113 + 127 + 131 + 137 + 139 + 149 + 151 + 157 + 163 + 167 + 173 + 179 + 181 + 191 + 193 + 197 + 199 + 211 + 223 + 227 + 229 + 233 + 239)/25.
%e a(6) = 304517 because 304517 = (304511 + 304517 + 304523)/3
%e = (304489 + 304501 + 304511 + 304517 + 304523 + 304537 + 304541)/7
%e = (304481 + 304489 + 304501 + 304511 + 304517 + 304523 + 304537 + 304541 + 304553)/9
%e = (303691 + ... + 304517 + ... + 305339)/135 = (303649 + ... + 304517 + ... + 305369)/143
%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]; t = Table[0, {15}]; Do[a = f[n]; If[a < 50 && t[[a + 1]] == 0, t[[a + 1]] = Prime[n]; Print[a + 1, " = ", Prime[n]]], {n, 32000}]; t
%Y Cf. A096693, A096705, A096706, A096707, A096708, A096709.
%K nonn
%O 0,1
%A _Robert G. Wilson v_, Jun 26 2004
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