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A096697
Balanced primes of order five.
17
53, 89, 157, 421, 433, 823, 991, 1297, 1709, 1873, 2347, 2411, 2441, 2729, 2797, 3617, 4793, 5059, 5417, 6343, 6781, 7583, 7933, 8581, 8861, 9029, 9857, 11213, 11953, 12329, 13229, 14081, 14411, 15767, 15889, 16561, 16889, 17029, 20297, 22469
OFFSET
1,1
LINKS
EXAMPLE
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).
MATHEMATICA
Transpose[ Select[ Partition[ Prime[ Range[5000]], 11, 1], #[[6]] == (#[[1]] + #[[2]] + #[[3]] + #[[4]] + #[[5]] + #[[7]] + #[[8]] + #[[9]] + #[[10]] + #[[11]])/10 &]][[6]]
(* Second program: *)
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 *)
PROG
(GAP) P:=Filtered([1..70000], IsPrime);;
a:=List(Filtered(List([0..3000], k->List([6..16], j->P[j-5+k])), i->
Sum(i)/11=i[6]), m->m[6]); # Muniru A Asiru, Feb 14 2018
(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
KEYWORD
nonn
AUTHOR
Robert G. Wilson v, Jun 26 2004
STATUS
approved