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A096697 Balanced primes of order five. 16

%I

%S 53,89,157,421,433,823,991,1297,1709,1873,2347,2411,2441,2729,2797,

%T 3617,4793,5059,5417,6343,6781,7583,7933,8581,8861,9029,9857,11213,

%U 11953,12329,13229,14081,14411,15767,15889,16561,16889,17029,20297,22469

%N Balanced primes of order five.

%H Aaron Toponce, <a href="/A096697/b096697.txt">Table of n, a(n) for n = 1..1000</a>

%e 53 is a member because 53 = (31 + 37 + 41 + 43 + 47 + 53 + 59 + 61 + 67 + 71 + 73)/11. 53 is also an order one balance prime (A006562) and an order three balanced prime (A082078), thus it has an balanced index of three (A096707).

%p P:=proc(q) local n; for n from 6 to q do

%p if add(ithprime(n-k),k=-5..5)=11*ithprime(n) then print(ithprime(n));

%p fi; od; end: P(10^6); # _Paolo P. Lava_, Mar 17 2014

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

%t (* Second program: *)

%t With[{k = 5}, Select[MapIndexed[{Prime[First@ #2 + k], #1} &, Mean /@ Partition[Prime@ Range[3000], 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..3000],k->List([6..16],j->P[j-5+k])),i->

%o Sum(i)/11=i[6]),m->m[6]); # _Muniru A Asiru_, Feb 14 2018

%o (PARI) isok(p) = {if (isprime(p), k = primepi(p); if (k > 5, sum(i=k-5, k+5, prime(i)) == 11*p;););} \\ _Michel Marcus_, Mar 07 2018

%Y Cf. A096693, A006562, A082077, A082078, A082079, A096698, A096699, A096700, A096701, A096702, A096703, A096704.

%K nonn

%O 1,1

%A _Robert G. Wilson v_, Jun 26 2004

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Last modified April 10 02:39 EDT 2020. Contains 333392 sequences. (Running on oeis4.)