A234358 Cubes t^3 = (p+q+r+s)/4 which are the arithmetic mean of four consecutive primes such that p < t^3 < q < r < s.

25934336, 194104539, 320013504, 332812557, 428661064, 8072216216, 8640364608, 11239424000, 16290480375, 17738739712, 26730899000, 44136677304, 46850670125, 68117264704, 114366627864, 119168121961

Offset: 1

Author

K. D. Bajpai, Dec 24 2013

Keywords

• nonn

Examples

			25934336 is in the sequence because 25934336 = 296^3 = (25934303+25934341+25934347+25934353)/4, the arithmetic mean of four consecutive primes.
320013504 is in the sequence because 320013504 = 684^3 = (320013479+320013509+320013511+320013517)/4, the arithmetic mean of four consecutive primes.
		

Links

• K. D. Bajpai, Table of n, a(n) for n = 1..3100

Crossrefs

Cf. A000578 (cubes: a(n) = 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).

Cf. A234256 (cubes: arithmetic mean of three consecutive primes).

Programs

Maple

KD := proc() local a,b,d,e,f,g; a:=n^3; b:=prevprime(a); d:=nextprime(a); e:=nextprime(d); f:=nextprime(e); g:=(b+d+e+f)/4;  if a=g then RETURN (a);  fi; end: seq(KD(), n=2..10000);

Extensions

Definition corrected by K. D. Bajpai, Jan 07 2014