A096697 - OEIS

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A096697

Balanced primes of order five.

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).

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