A081415 Triply balanced primes: primes which are averages of both their immediate neighbor, their second neighbors and their third neighbors.

683783, 1056317, 1100261, 2241709, 2815301, 4746359, 10009049, 12003209, 13810981, 14907649, 15403009, 15730067, 16595081, 17518201, 19755301, 20378327, 21006487, 21574453, 21579983, 22237121, 22625179, 25876901

Offset

1,1

Comments

Equivalently, primes which are balanced primes of orders 1, 2, and 3. - Muniru A Asiru, Apr 08 2018

Links

Jud McCranie, Table of n, a(n) for n = 1..1000

Wikipedia, Balanced prime

Example

p = 683383: 683747 + ... + p + .. + 683819 = 7p; 683759 + .. + p + .. + 683807 = 5p; 683777 + p + 683789 = 3p.

Mathematica

a = {}; Do[p = 2Prime[n]; If[p == Prime[n - 1] + Prime[n + 1], If[p == Prime[n - 2] + Prime[n + 2], If[p == Prime[n - 3] + Prime[n + 3], {n, 5, 1100000}] (* Robert G. Wilson v, Jun 28 2004 *)
Transpose[Select[Partition[Prime[Range[1620000]], 7, 1], (#[[1]]+#[[7]])/2 == (#[[2]]+#[[6]])/2==(#[[3]]+#[[5]])/2==#[[4]]&]][[4]] (* Harvey P. Dale, Sep 13 2013 *)

Prog

(GAP) P:=Filtered([1, 3..3*10^7+1], IsPrime);;
a:=Intersection(List([1, 2, 3], b->List(Filtered(List([0..Length(P)-(2*b+1)], k->List([1..2*b+1], j->P[j+k])), i->Sum(i)/(2*b+1)=i[b+1]), m->m[b+1]))); # Muniru A Asiru, Apr 08 2018

Crossrefs

Cf. A006562, A051795, A055380, A096710.

Sequence in context: A203713 A236986 A258607 * A354447 A101698 A323805

Adjacent sequences: A081412 A081413 A081414 * A081416 A081417 A081418

Keyword

nonn

Author

Labos Elemer, Apr 02 2003

Status

approved