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%I #15 Feb 16 2024 10:05:16
%S 173,353,631,827,3329,4723,13693,17789,20947,21059,21503,23563,23599,
%T 27751,29759,35419,36781,37991,44939,52021,57163,57269,57719,59663,
%U 68713,70529,70879,71399,75541,76949,78301,79621,94399,101929,104759
%N Balanced primes of order eleven.
%H Muniru A Asiru, <a href="/A096703/b096703.txt">Table of n, a(n) for n = 1..5000</a>
%e 173 is a member because 173 = (109 + 113 + 127 + 131 + 137 + 139 + 149 + 151 + 157 + 163 + 167 + 173 + 179 + 181 + 191 + 193 + 197 + 199 + 211 + 223 + 227 + 229 + 233)/23 = 3979/23.
%t Transpose[ Select[ Partition[ Prime[ Range[10000]], 23, 1], #[[12]] == (#[[1]] + #[[2]] + #[[3]] + #[[4]] + #[[5]] + #[[6]] + #[[7]] + #[[8]] + #[[9]] + #[[10]] + #[[11]] + #[[13]] + #[[14]] + #[[15]] + #[[16]] + #[[17]] + #[[18]] + #[[19]] + #[[20]] + #[[21]] + #[[22]] + #[[23]])/22 &]][[12]]
%t Transpose[Select[Partition[Prime[Range[11000]],23,1],Mean[#] == #[[12]]&]][[12]] (* _Harvey P. Dale_, Nov 06 2011 *)
%o (GAP) P:=Filtered([1..150000],IsPrime);;
%o a:=List(Filtered(List([0..12000],k->List([1..23],j->P[j+k])),i->Sum(i)/23=i[12]),m->m[12]); # _Muniru A Asiru_, Mar 04 2018
%Y Cf. A096693, A006562, A082077, A082078, A082079, A096697, A096698, A096699, A096700, A096701, A096702, A096704.
%K nonn
%O 1,1
%A _Robert G. Wilson v_, Jun 26 2004
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