A176229 -id:A176229 - cp's OEIS frontend

A178228 Numbers k such that (k^3 - 2, k^3 + 2) is a pair of cousin primes (see A178227).

129, 189, 369, 435, 549, 555, 561, 819, 1245, 1491, 1719, 1779, 1839, 1875, 1935, 2175, 2289, 2415, 2451, 2595, 2709, 2769, 3141, 3441, 4401, 4611, 4851, 5655, 5775, 6075, 6099, 6795, 6969, 7125, 7239, 7365, 8109, 8139, 8325, 8361, 8385, 8535, 8685, 9591, 9765

Offset: 1

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

nonn

Necessarily k is an odd multiple of 3, Least significant digit of k is e = 1, 5 or 9 (3^3 - 2, 7^3 + 2 are multiples of 5).

			189 is a term since 189^3 - 2 = 6751267 = prime(460792), 189^3 + 2 = 6751271 = prime(460793).
12471 is a term since 12471^3 - 2 = 1939562763109 = prime(i), i = 71166976775, 12471^3 + 2 = 1939562763113 = prime(i+1).

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

Cf. A023200, A046132, A090121, A164834, A172494, A174370, A176130, A176229, A178227.

Select[Range[10^4], And @@ PrimeQ[#^3 + {-2, 2}] &] (* Amiram Eldar, Dec 24 2019 *)

for(n=1,10000,my(p1=n^3-2,p2=n^3+2);if(isprime(p1)&&isprime(p2)&&ispower((p1+p2)/2,3),print1(n,", "))) \\ Hugo Pfoertner, Dec 24 2019

Edited by N. J. A. Sloane, May 23 2010

a(1) and a(21) inserted by Amiram Eldar, Dec 24 2019

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

Original entry on oeis.org

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

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

nonn

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

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

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

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

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

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

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

Corrected by D. S. McNeil, Nov 24 2010

More terms from Amiram Eldar, Dec 24 2019

cp's OEIS Frontend

A178228 Numbers k such that (k^3 - 2, k^3 + 2) is a pair of cousin primes (see A178227).

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