A145317 Numbers n such that prime[(n + 1)^2] - prime[n^2] is a perfect cube.

79, 10288, 16181, 306998, 394021

Offset

1,1

Comments

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

Links

Table of n, a(n) for n=1..5.

Example

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.

Mathematica

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

Crossrefs

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

Sequence in context: A116235 A123814 A265446 * A363515 A251365 A023343

Adjacent sequences: A145314 A145315 A145316 * A145318 A145319 A145320

Keyword

nonn

Author

Zak Seidov, Oct 07 2008

Status

approved