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

1,1

Comments

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

Links

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

Formula

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

Example

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

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A237140 A129477 A235930 * A154709 A344356 A344357

Adjacent sequences: A178224 A178225 A178226 * A178228 A178229 A178230

Keyword

nonn

Author

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

Extensions

Corrected by D. S. McNeil, Nov 24 2010

More terms from Amiram Eldar, Dec 24 2019

Status

approved