%I #30 Feb 16 2024 10:05:02

%S 71,211,397,409,1487,1559,2281,4397,4937,5347,5857,7577,10399,11369,

%T 12583,14843,19391,21739,21787,22067,22469,23789,25639,27329,29537,

%U 29867,30197,30911,33347,33931,34267,35099,36131,36691,37549,38671

%N Balanced primes of order six.

%H Aaron Toponce, <a href="/A096698/b096698.txt">Table of n, a(n) for n = 1..1000</a>

%e 71 is a member because 71 = (43 + 47 + 53 + 59 + 61 + 67 + 71 + 73 + 79 + 83 + 89 + 97 + 101)/13.

%t Transpose[ Select[ Partition[ Prime[ Range[5000]], 13, 1], #[[7]] == (#[[1]] + #[[2]] + #[[3]] + #[[4]] + #[[5]] + #[[6]] + #[[8]] + #[[9]] + #[[10]] + #[[11]] + #[[12]] + #[[13]])/12 &]][[7]]

%t Transpose[Select[Partition[Prime[Range[5000]],13,1],Total[#]/13==#[[7]]&]][[7]] (* _Harvey P. Dale_, Feb 25 2011 *)

%o (GAP) P:=Filtered([1..90000],IsPrime);;

%o b:=6;;

%o a:=List(Filtered(List([0..5000],k->List([b+1..3*b+1],j->P[j-b+k])),i->Sum(i)/(2*b+1)=i[b+1]),m->m[b+1]); # _Muniru A Asiru_, Feb 15 2018

%o (PARI) isok(p) = {if (isprime(p), k = primepi(p); if (k >6, sum(i=k-6, k+6, prime(i)) == 13*p;););} \\ _Michel Marcus_, Mar 07 2018

%Y Cf. A096693, A006562, A082077, A082078, A082079, A096697, A096699, A096700, A096701, A096702, A096703, A096704.

%K nonn

%O 1,1

%A _Robert G. Wilson v_, Jun 26 2004