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A178228
Numbers k such that (k^3 - 2, k^3 + 2) is a pair of cousin primes (see A178227).
6
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
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
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