A178227 Lesser of a pair (p,p+4) of cousin primes whose arithmetic mean p+2 is a cube.

2146687, 6751267, 50243407, 82312873, 165469147, 170953873, 176558479, 549353257, 1929781123, 3314613769, 5079577957, 5630252137, 6219352717, 6591796873, 7245075373, 10289109373, 11993263567, 14084823373, 14724139849, 17474794873, 19880486827, 21230922607, 30988732219

Offset: 1

Author

Ulrich Krug (leuchtfeuer37(AT)gmx.de), May 23 2010

Keywords

• nonn

Comments

p = n^3 - 2, p and p+4 are "near(est) cube" primes as n^3 -/+ 1 = (n -/+ 1) * (n^2 +/- n + 1).

Examples

			p = 2146687 is a term, as p + 2 = 129^3 and both p = 129^3 - 2 and p + 4 = 129^3 + 2 are prime.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A023200, A046132, A172494, A174370, A176130, A178228, A176229.

Programs

Mathematica

Select[Range[2300]^3 - 2, And @@ PrimeQ[# + {0, 4}] &] (* Amiram Eldar, Dec 24 2019 *)

PARI

isok(p) = isprime(p) && (q=nextprime(p+1)) && (q-p==4) && ispower(p+2, 3); \\ Michel Marcus, Nov 27 2016

Formula

a(n) = A178228(n)^3 - 2. - Amiram Eldar, Dec 24 2019

Extensions

Corrected by D. S. McNeil, Nov 24 2010

More terms from Amiram Eldar, Dec 24 2019