

A081415


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


9



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



