A145317 - OEIS

%I #4 Dec 13 2012 15:29:12

%S 79,10288,16181,306998,394021

%N Numbers n such that prime[(n + 1)^2] - prime[n^2] is a perfect cube.

%C n such that A011757(n + 1) - A011757(n) is a perfect cube

%e p1=prime[(n + 1)^2], p= prime[n^2], p1-p2=q^3: n = 79, p1 = 63809, p = 62081, q = 12; n = 10288, p1 = 2163941687, p = 2163502711, q = 76; n = 16181, p1 = 5602364903, p = 5601635903, q = 90; n = 306998, p1=2596139184841, p = 2596121608841, q = 260. n = 394021, p1 = 4357072887373, p = 4357049981069, q = 284. Next n, if any, is > 500000.

%t Select[Range[400000],IntegerQ[(Prime[(#+1)^2]-Prime[#^2])^(1/3)]&] (* _Harvey P. Dale_, Dec 13 2012 *)

%Y A145290 prime[(n + 1)^2] - prime[n^2] is a perfect square, A011757 prime(n^2).

%K nonn

%O 1,1

%A _Zak Seidov_, Oct 07 2008