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%I #23 Feb 28 2021 16:37:11
%S 129,189,369,435,549,555,561,819,1245,1491,1719,1779,1839,1875,1935,
%T 2175,2289,2415,2451,2595,2709,2769,3141,3441,4401,4611,4851,5655,
%U 5775,6075,6099,6795,6969,7125,7239,7365,8109,8139,8325,8361,8385,8535,8685,9591,9765
%N Numbers k such that (k^3 - 2, k^3 + 2) is a pair of cousin primes (see A178227).
%C 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).
%H Amiram Eldar, <a href="/A178228/b178228.txt">Table of n, a(n) for n = 1..10000</a>
%e 189 is a term since 189^3 - 2 = 6751267 = prime(460792), 189^3 + 2 = 6751271 = prime(460793).
%e 12471 is a term since 12471^3 - 2 = 1939562763109 = prime(i), i = 71166976775, 12471^3 + 2 = 1939562763113 = prime(i+1).
%t Select[Range[10^4], And @@ PrimeQ[#^3 + {-2, 2}] &] (* _Amiram Eldar_, Dec 24 2019 *)
%o (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
%Y Cf. A023200, A046132, A090121, A164834, A172494, A174370, A176130, A176229, A178227.
%K nonn
%O 1,1
%A Ulrich Krug (leuchtfeuer37(AT)gmx.de), May 23 2010
%E Edited by _N. J. A. Sloane_, May 23 2010
%E a(1) and a(21) inserted by _Amiram Eldar_, Dec 24 2019
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