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A234240 Cubes which are arithmetic mean of two consecutive primes. 8
64, 1728, 4096, 17576, 21952, 46656, 110592, 195112, 287496, 314432, 405224, 474552, 1061208, 1191016, 1404928, 1601613, 1906624, 2000376, 2146689, 2197000, 3241792, 3511808, 4913000, 5268024, 6229504, 6751269, 6859000, 7077888, 11239424, 20346417, 21952000 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

K. D. Bajpai and Alois P. Heinz, Table of n, a(n) for n = 1..1000 (terms n = 1..57 from K. D. Bajpai)

FORMULA

a(n) = A075191(n)^3.

EXAMPLE

64 is in the sequence because cube 64 = 4^3 = (61+67)/2 is arithmetic mean of two consecutive primes.

1728 is in the sequence because 1728 = 12^3 = (1723+1733)/2.

MAPLE

a:= proc(n) option remember; local k, kk, p, q;

      for k from 1 +`if`(n=1, 1, iroot(a(n-1), 3))

      do kk:= k^3; p, q:= prevprime(kk), nextprime(kk);

         if (p+q)/2=kk then return kk fi

      od

    end:

seq(a(n), n=1..60);  # Alois P. Heinz, Dec 21 2013

MATHEMATICA

Select[Mean/@Partition[Prime[Range[1500000]], 2, 1], IntegerQ[Surd[#, 3]]&] (* Harvey P. Dale, Oct 08 2014 *)

Select[Range[300]^3, #==Mean[{NextPrime[#], NextPrime[#, -1]}]&] (* Harvey P. Dale, Sep 02 2015 *)

PROG

(PARI) is(n)=nextprime(n)+precprime(n)==2*n && ispower(n, 3)

for(n=8, 1e4, if(is(n^3), print1(n^3", "))) \\ Charles R Greathouse IV, Aug 25 2014

CROSSREFS

Cf. A000578, A062703, A069495, A075191.

Sequence in context: A316875 A317603 A269660 * A017115 A269203 A005609

Adjacent sequences:  A234237 A234238 A234239 * A234241 A234242 A234243

KEYWORD

nonn

AUTHOR

K. D. Bajpai, Dec 21 2013

STATUS

approved

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Last modified April 20 02:46 EDT 2019. Contains 322291 sequences. (Running on oeis4.)