A300365 Balanced primes of order fourteen.

5297, 15647, 22073, 22501, 26309, 34721, 43499, 44111, 48809, 57529, 58171, 66797, 69151, 70199, 74551, 76493, 86959, 91297, 93169, 93199, 94343, 102217, 110777, 112289, 113093, 132361, 133493, 135461, 139921, 146021, 155303, 156521, 162557, 163753, 163789

Offset: 1

Author

Muniru A Asiru, Mar 04 2018

Keywords

• nonn

Examples

			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.
		

Links

• Muniru A Asiru, Table of n, a(n) for n = 1..6600

Crossrefs

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).

Programs

GAP

P:=Filtered([1..200000],IsPrime);;
a:=List(Filtered(List([0..17000],k->List([1..29],j->P[j+k])),i->Sum(i)/29=i[15]),m->m[15]);

Mathematica

Module[{bal=14,nn=16000},Select[Partition[Prime[Range[nn]],2bal+1,1],Mean[#]==#[[bal+1]]&]][[;;,15]] (* Harvey P. Dale, Jul 07 2023 *)