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

1,1

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).

Links

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

Example

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).

Mathematica

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

Prog

(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

Crossrefs

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

Sequence in context: A127337 A185347 A034072 * A235879 A157951 A043383

Adjacent sequences: A178225 A178226 A178227 * A178229 A178230 A178231

Keyword

nonn

Author

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

Extensions

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

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

Status

approved