A096698 Balanced primes of order six.

71, 211, 397, 409, 1487, 1559, 2281, 4397, 4937, 5347, 5857, 7577, 10399, 11369, 12583, 14843, 19391, 21739, 21787, 22067, 22469, 23789, 25639, 27329, 29537, 29867, 30197, 30911, 33347, 33931, 34267, 35099, 36131, 36691, 37549, 38671

Offset: 1

Author

Robert G. Wilson v, Jun 26 2004

Keywords

• nonn

Examples

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

Links

• Aaron Toponce, Table of n, a(n) for n = 1..1000

Crossrefs

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

Programs

GAP

P:=Filtered([1..90000],IsPrime);;
b:=6;;
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

Mathematica

Transpose[ Select[ Partition[ Prime[ Range[5000]], 13, 1], #[[7]] == (#[[1]] + #[[2]] + #[[3]] + #[[4]] + #[[5]] + #[[6]] + #[[8]] + #[[9]] + #[[10]] + #[[11]] + #[[12]] + #[[13]])/12 &]][[7]]
Transpose[Select[Partition[Prime[Range[5000]],13,1],Total[#]/13==#[[7]]&]][[7]]  (* Harvey P. Dale, Feb 25 2011 *)

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