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 A096697 Balanced primes of order five. 16
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Aaron Toponce, Table of n, a(n) for n = 1..1000 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). MAPLE P:=proc(q) local n; for n from 6 to q do if add(ithprime(n-k), k=-5..5)=11*ithprime(n) then print(ithprime(n)); fi; od; end: P(10^6); # Paolo P. Lava, Mar 17 2014 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 CROSSREFS Cf. A096693, A006562, A082077, A082078, A082079, A096698, A096699, A096700, A096701, A096702, A096703, A096704. Sequence in context: A119289 A124282 A137869 * A033234 A266845 A238678 Adjacent sequences:  A096694 A096695 A096696 * A096698 A096699 A096700 KEYWORD nonn AUTHOR Robert G. Wilson v, Jun 26 2004 STATUS approved

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Last modified February 27 10:15 EST 2020. Contains 332304 sequences. (Running on oeis4.)