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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.

%I A234358 #12 Jun 25 2022 17:08:18
%S A234358 25934336,194104539,320013504,332812557,428661064,8072216216,
%T A234358 8640364608,11239424000,16290480375,17738739712,26730899000,
%U A234358 44136677304,46850670125,68117264704,114366627864,119168121961
%N 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.
%H A234358 K. D. Bajpai, <a href="/A234358/b234358.txt">Table of n, a(n) for n = 1..3100</a>
%e A234358 25934336 is in the sequence because 25934336 = 296^3 = (25934303+25934341+25934347+25934353)/4, the arithmetic mean of four consecutive primes.
%e A234358 320013504 is in the sequence because 320013504 = 684^3 = (320013479+320013509+320013511+320013517)/4, the arithmetic mean of four consecutive primes.
%p A234358 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);
%Y A234358 Cf. A000578 (cubes:  a(n) = n^3).
%Y A234358 Cf. A062703 (squares: sum of two consecutive primes).
%Y A234358 Cf. A069495 (squares: arithmetic mean of two consecutive primes).
%Y A234358 Cf. A234240 (cubes: arithmetic mean of two consecutive primes).
%Y A234358 Cf. A234256 (cubes: arithmetic mean of three consecutive primes).
%K A234358 nonn
%O A234358 1,1
%A A234358 _K. D. Bajpai_, Dec 24 2013
%E A234358 Definition corrected by _K. D. Bajpai_, Jan 07 2014