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

Author

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

Keywords

• nonn

Comments

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).

Examples

			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).
		

Links

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

Crossrefs

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

Programs

Mathematica

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

PARI

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

Extensions

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

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