A096699 Balanced primes of order seven.

29, 977, 1381, 1439, 3109, 3539, 4357, 4397, 5563, 7159, 8273, 8737, 10711, 11117, 13109, 13841, 15101, 18731, 18839, 20543, 21391, 21851, 23459, 24877, 27653, 28477, 28697, 30677, 32029, 32971, 34631, 35863, 36979, 37019, 37529, 38189

Offset: 1

Author

Robert G. Wilson v, Jun 26 2004

Keywords

• nonn

Examples

			29 is a member because 29 = (5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 + 59)/15.
		

Links

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

Crossrefs

Cf. A096693, A006562, A082077, A082078, A082079, A096697, A096698, A096700, A096701, A096702, A096703, A096704.

Programs

GAP

P:=Filtered([1..70000],IsPrime);;
a:=List(Filtered(List([0..5000],k->List([8..22],j->P[j-7+k])),i->
Sum(i)/15=i[8]),m->m[8]); # Muniru A Asiru, Feb 14 2018

Mathematica

Transpose[ Select[ Partition[ Prime[ Range[5000]], 15, 1], #[[8]] == (#[[1]] + #[[2]] + #[[3]] + #[[4]] + #[[5]] + #[[6]] + #[[7]] + #[[9]] + #[[10]] + #[[11]] + #[[12]] + #[[13]] + #[[14]] + #[[15]])/14 &]][[8]]
(* Second program: *)
With[{k = 7}, Select[MapIndexed[{Prime[First@ #2 + k], #1} &, Mean /@ Partition[Prime@ Range[5000], 2 k + 1, 1]], SameQ @@ # &][[All, 1]]] (* Michael De Vlieger, Feb 15 2018 *)

PARI

isok(p) = {if (isprime(p), k = primepi(p); if (k > 7, sum(i=k-7, k+7, prime(i)) == 15*p;););} \\ Michel Marcus, Mar 07 2018