

A051795


Doubly balanced primes: primes which are averages of both their immediate and their second neighbors.


15



18731, 25621, 28069, 30059, 31051, 44741, 76913, 97441, 103669, 106681, 118831, 128449, 135089, 182549, 202999, 240491, 245771, 249199, 267569, 295387, 347329, 372751, 381401, 435751, 451337, 455419, 471521, 478099, 498301, 516877, 526441
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OFFSET

1,1


COMMENTS

Could also be called overbalanced or [3,5]balanced primes: balanced primes which are equally average of 3,5 consecutive prime neighbors as follows: a(n)=[q+a(n)+r]/3=[p+q+a(n)+r+s]/5 See 3balanced=A006562;[3,5,7]balanced=A081415.  Labos Elemer, Apr 02 2003


LINKS

Jud McCranie and Sebastian Petzelberger, Table of n, a(n) for n = 1..10000 (first 1000 terms from Jud McCranie)


EXAMPLE

25621 belongs to the sequence because 25621 = (25609 + 25633)/2 = (25603 + 25609 + 25633 + 25639)/4.


MAPLE

P:=proc(q) local n; for n from 3 to q do
if (ithprime(n1)+ithprime(n+1))/2=ithprime(n) and (ithprime(n2)+ithprime(n+2))/2=ithprime(n) then print(ithprime(n)); fi; od; end: P(10^6); # Paolo P. Lava, Mar 17 2014


MATHEMATICA

Do[s=Prime[n1]+Prime[n]+Prime[n+1]; s1=Prime[n2]+s+Prime[n+2]; If[Equal[s/3, Prime[n]]&&Equal[s1/5, Prime[n]], Print[Prime[n]]], {n, 4, 1000000}] (* Labos Elemer *)
Transpose[Select[Partition[Prime[Range[50000]], 5, 1], (#[[1]]+#[[5]])/2 == (#[[2]]+#[[4]])/2 == #[[3]]&]][[3]] (* Harvey P. Dale, Sep 13 2013 *)


CROSSREFS

Cf. A006562, A081415, A096710, A055380.
Sequence in context: A267028 A226150 A081416 * A338949 A269886 A269765
Adjacent sequences: A051792 A051793 A051794 * A051796 A051797 A051798


KEYWORD

easy,nonn


AUTHOR

Harvey P. Dale, Dec 10 1999


STATUS

approved



