A082078 Balanced primes of order three.

17, 53, 157, 173, 193, 229, 349, 439, 607, 659, 701, 709, 977, 1153, 1187, 1301, 1619, 2281, 2287, 2293, 2671, 2819, 2843, 3067, 3313, 3539, 3673, 3727, 3833, 4013, 4051, 4517, 4951, 5101, 5897, 6079, 6203, 6211, 6323, 6679, 6869, 7321, 7589, 7643, 7907

Offset

1,1

Comments

The arithmetic mean of 6 primes in its "neighborhood"; not to be confused with 'Triply balanced primes' (A081415).

A balanced prime of order three is not necessarily balanced of order one (A006562) or two (A082077), etc. [Typo corrected by Zak Seidov, Jul 23 2008]

Links

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

Example

p = 53 = (41 + 43 + 47 + 53 + 59 + 61 + 67)/7 = 371/7 i.e. it is the arithmetic mean.

Mathematica

Do[s3=Prime[n]+Prime[n+1]+Prime[n+2]; s5=Prime[n-1]+s3+Prime[n+3]; s7=Prime[n-2]+s5+Prime[n+4]; If[Equal[s7/7, Prime[n+1]], Print[Prime[n+1]]], {n, 3, 5000}]
(* Second program: *)
With[{k = 3}, Select[MapIndexed[{Prime[First@ #2 + k], #1} &, Mean /@ Partition[Prime@ Range[10^3], 2 k + 1, 1]], SameQ @@ # &][[All, 1]]]  (* Michael De Vlieger, Feb 15 2018 *)
Select[Partition[Prime[Range[1500]], 7, 1], Mean[#]==#[[4]]&][[All, 4]] (* Harvey P. Dale, Jul 01 2022 *)

Prog

(GAP) P:=Filtered([1..10000], IsPrime);;
a:=List(Filtered(List([0..1000], k->List([4..10], j->P[j-3+k])), i->
Sum(i)/7=i[4]), m->m[4]); # Muniru A Asiru, Feb 14 2018
(PARI) isok(p) = {if (isprime(p), k = primepi(p); if (k > 3, sum(i=k-3, k+3, prime(i)) == 7*p; ); ); } \\ Michel Marcus, Mar 07 2018

Crossrefs

Cf. A006562, A082077, A082079, A096697, A096698, A096699, A096700, A096701, A096702, A096703, A096704.

Cf. A096693, A082080, A081415, A051795, A006562.

Sequence in context: A180456 A154409 A033213 * A107175 A244270 A244271

Adjacent sequences: A082075 A082076 A082077 * A082079 A082080 A082081

Keyword

nonn

Author

Labos Elemer, Apr 08 2003

Status

approved