|
|
A096699
|
|
Balanced primes of order seven.
|
|
17
|
|
|
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
|
|
|
EXAMPLE
|
29 is a member because 29 = (5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 + 59)/15.
|
|
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->
(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.
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|