A234256 Cubes t^3 = (p+q+r)/3 which are the arithmetic mean of three consecutive primes such that p < t^3 < q < r.

5735339, 10503459, 73560059, 253636137, 393832837, 761048497, 791453125, 1064332261, 1829276567, 2014698447, 2487813875, 2893640625, 4533086375, 7845011803, 14437662875, 45998156287, 55611739513, 62429032063, 63378025803, 72877493233, 87115050737, 104154702625

Offset: 1

Author

K. D. Bajpai, Dec 22 2013

Keywords

• nonn

Examples

			5735339 is in the sequence because 5735339 = 179^3 = (5735291+5735357+5735369)/3, the arithmetic mean of three consecutive primes.
10503459 is in the sequence because 10503459 = 219^3 = (10503443+10503461+10503473)/3, the arithmetic mean of three consecutive primes.
		

Links

• K. D. Bajpai, Table of n, a(n) for n = 1..3680

Crossrefs

Cf. A000578 (cubes: n^3).

Cf. A062703 (squares: sum of two consecutive primes).

Cf. A069495 (squares: arithmetic mean of two consecutive primes).

Cf. A234240 (cubes: arithmetic mean of two consecutive primes).

Programs

Maple

with(numtheory):KD := proc() local a,b,d,e,f; a:=n^3; b:=prevprime(a); d:=nextprime(a); e:=nextprime(d);  f:=(b+d+e)/3; if  a=f then RETURN (a);  fi;  end: seq(KD(), n=2..10000);

PARI

list(lim)=my(v=List(), p=2, q=3, t); forprime(r=5, nextprime(nextprime(lim\3+1)+1), t=(p+q+r)/3; if(denominator(t)==1 && ispower(t,3) && t < q, listput(v, t)); p=q; q=r); Vec(v) \\ Charles R Greathouse IV, Jan 03 2014

Extensions

Definition corrected by Michel Marcus and Charles R Greathouse IV, Jan 03 2014