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%I #10 Jul 07 2023 19:08:33
%S 5297,15647,22073,22501,26309,34721,43499,44111,48809,57529,58171,
%T 66797,69151,70199,74551,76493,86959,91297,93169,93199,94343,102217,
%U 110777,112289,113093,132361,133493,135461,139921,146021,155303,156521,162557,163753,163789
%N Balanced primes of order fourteen.
%H Muniru A Asiru, <a href="/A300365/b300365.txt">Table of n, a(n) for n = 1..6600</a>
%e 5297 is a member because 5297 = 5167 + 5171 + 5179 + 5189 + 5197 + 5209 + 5227 + 5231 + 5233 + 5237 + 5261 + 5273 + 5279 + 5281 + 5297 + 5303 + 5309 + 5323 + 5333 + 5347 + 5351 + 5381 + 5387 + 5393 + 5399 + 5407 + 5413 + 5417 + 5419 = 153613/29.
%t Module[{bal=14,nn=16000},Select[Partition[Prime[Range[nn]],2bal+1,1],Mean[#]==#[[bal+1]]&]][[;;,15]] (* _Harvey P. Dale_, Jul 07 2023 *)
%o (GAP) P:=Filtered([1..200000],IsPrime);;
%o a:=List(Filtered(List([0..17000],k->List([1..29],j->P[j+k])),i->Sum(i)/29=i[15]),m->m[15]);
%Y Cf. Balanced primes of order b: A006562 (b=1), A082077 (b=2), A082078 (b=3), A082079 (b=4), A096697 (b=5), A096698 (b=6), A096699 (b=7), A096700 (b=8), A096701 (b=9), A096702 (b=10), A096703 (b=11), A096704 (b=12), A300364 (b=13) this sequence (b=14).
%K nonn
%O 1,1
%A _Muniru A Asiru_, Mar 04 2018
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