

A051795


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


13



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


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}] (From Labos)
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: A248065 A226150 A081416 * A236015 A237764 A243134
Adjacent sequences: A051792 A051793 A051794 * A051796 A051797 A051798


KEYWORD

easy,nonn


AUTHOR

Harvey P. Dale, Dec 10 1999


STATUS

approved



