A096701 - OEIS

%I #21 Feb 16 2024 10:04:54

%S 983,2351,4019,4093,4957,8731,10009,10211,10271,11549,11593,12809,

%T 13831,17971,21647,25633,30313,32411,33911,34283,37277,37511,38711,

%U 39749,41617,41737,42299,46643,48809,49121,49451,51599,53381,54541,54559

%N Balanced primes of order nine.

%H Zak Seidov, <a href="/A096701/b096701.txt">Table of n, a(n) for n = 1..10000</a>

%e 983 is a member because 983 = (919 + 929 + 937 + 941 + 947 + 953 + 967 + 971 + 977 + 983 + 991 + 997 + 1009 + 1013 + 1019 + 1021 + 1031 + 1033 + 1039)/19 = 18677/19.

%t Transpose[ Select[ Partition[ Prime[ Range[7500]], 19, 1], #[[10]] == (#[[1]] + #[[2]] + #[[3]] + #[[4]] + #[[5]] + #[[6]] + #[[7]] + #[[8]] + #[[9]] + #[[11]] + #[[12]] + #[[13]] + #[[14]] + #[[15]] + #[[16]] + #[[17]] + #[[18]] + #[[19]])/18 &]][[10]]

%t #[[10]] & /@ Select[Partition[Prime[Range[7500]], 19, 1], #[[10]] == Mean[#] &] (* _Zak Seidov_, Mar 01 2017 *)

%o (GAP) P:=Filtered([1..80000],IsPrime);;

%o a:=List(Filtered(List([0..6000],k->List([10..28],j->P[j-9+k])),i->

%o Sum(i)/19=i[10]),m->m[10]); # _Muniru A Asiru_, Feb 14 2018

%o (PARI) isok(p) = {if (isprime(p), k = primepi(p); if (k > 9, sum(i=k-9, k+9, prime(i)) == 19*p;););} \\ _Michel Marcus_, Mar 07 2018

%Y Cf. A096693, A006562, A082077, A082078, A082079, A096697, A096698, A096699, A096700, A096702, A096703, A096704.

%K nonn

%O 1,1

%A _Robert G. Wilson v_, Jun 26 2004