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%I #26 Feb 16 2024 10:05:08
%S 29,977,1381,1439,3109,3539,4357,4397,5563,7159,8273,8737,10711,11117,
%T 13109,13841,15101,18731,18839,20543,21391,21851,23459,24877,27653,
%U 28477,28697,30677,32029,32971,34631,35863,36979,37019,37529,38189
%N Balanced primes of order seven.
%H Aaron Toponce, <a href="/A096699/b096699.txt">Table of n, a(n) for n = 1..1000</a>
%e 29 is a member because 29 = (5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 + 59)/15.
%t 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]]
%t (* Second program: *)
%t 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 *)
%o (GAP) P:=Filtered([1..70000],IsPrime);;
%o a:=List(Filtered(List([0..5000],k->List([8..22],j->P[j-7+k])),i->
%o Sum(i)/15=i[8]),m->m[8]); # _Muniru A Asiru_, Feb 14 2018
%o (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
%Y Cf. A096693, A006562, A082077, A082078, A082079, A096697, A096698, A096700, A096701, A096702, A096703, A096704.
%K nonn
%O 1,1
%A _Robert G. Wilson v_, Jun 26 2004
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