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A096699 Balanced primes of order seven. 16
29, 977, 1381, 1439, 3109, 3539, 4357, 4397, 5563, 7159, 8273, 8737, 10711, 11117, 13109, 13841, 15101, 18731, 18839, 20543, 21391, 21851, 23459, 24877, 27653, 28477, 28697, 30677, 32029, 32971, 34631, 35863, 36979, 37019, 37529, 38189 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Aaron Toponce, Table of n, a(n) for n = 1..1000

EXAMPLE

29 is a member because 29 = (5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 + 59)/15.

MAPLE

P:=proc(q) local n; for n from 8 to q do

if add(ithprime(n-k), k=-7..7)=15*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]], 15, 1], #[[8]] == (#[[1]] + #[[2]] + #[[3]] + #[[4]] + #[[5]] + #[[6]] + #[[7]] + #[[9]] + #[[10]] + #[[11]] + #[[12]] + #[[13]] + #[[14]] + #[[15]])/14 &]][[8]]

(* Second program: *)

With[{k = 7}, Select[MapIndexed[{Prime[First@ #2 + k], #1} &, Mean /@ Partition[Prime@ Range[5000], 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..5000], k->List([8..22], j->P[j-7+k])), i->

Sum(i)/15=i[8]), m->m[8]); # Muniru A Asiru, Feb 14 2018

(PARI) isok(p) = {if (isprime(p), k = primepi(p); if (k > 7, sum(i=k-7, k+7, prime(i)) == 15*p; ); ); } \\ Michel Marcus, Mar 07 2018

CROSSREFS

Cf. A096693, A006562, A082077, A082078, A082079, A096697, A096698, A096700, A096701, A096702, A096703, A096704.

Sequence in context: A324432 A167738 A107964 * A316708 A218807 A218193

Adjacent sequences:  A096696 A096697 A096698 * A096700 A096701 A096702

KEYWORD

nonn

AUTHOR

Robert G. Wilson v, Jun 26 2004

STATUS

approved

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Last modified November 13 04:20 EST 2019. Contains 329085 sequences. (Running on oeis4.)