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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 (list; graph; refs; listen; history; text; internal format)
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 3-balanced=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(n-1)+ithprime(n+1))/2=ithprime(n) and (ithprime(n-2)+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[n-1]+Prime[n]+Prime[n+1]; s1=Prime[n-2]+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: A237700 A226150 A081416 * A236015 A237764 A212077

Adjacent sequences:  A051792 A051793 A051794 * A051796 A051797 A051798

KEYWORD

easy,nonn

AUTHOR

Harvey P. Dale, Dec 10 1999

STATUS

approved

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Last modified April 24 14:19 EDT 2014. Contains 240985 sequences.