|
%I #17 Dec 24 2019 08:26:51
%S 2146687,6751267,50243407,82312873,165469147,170953873,176558479,
%T 549353257,1929781123,3314613769,5079577957,5630252137,6219352717,
%U 6591796873,7245075373,10289109373,11993263567,14084823373,14724139849,17474794873,19880486827,21230922607,30988732219
%N Lesser of a pair (p,p+4) of cousin primes whose arithmetic mean p+2 is a cube.
%C p = n^3 - 2, p and p+4 are "near(est) cube" primes as n^3 -/+ 1 = (n -/+ 1) * (n^2 +/- n + 1).
%H Amiram Eldar, <a href="/A178227/b178227.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = A178228(n)^3 - 2. - _Amiram Eldar_, Dec 24 2019
%e p = 2146687 is a term, as p + 2 = 129^3 and both p = 129^3 - 2 and p + 4 = 129^3 + 2 are prime.
%t Select[Range[2300]^3 - 2, And @@ PrimeQ[# + {0, 4}] &] (* _Amiram Eldar_, Dec 24 2019 *)
%o (PARI) isok(p) = isprime(p) && (q=nextprime(p+1)) && (q-p==4) && ispower(p+2, 3); \\ _Michel Marcus_, Nov 27 2016
%Y Cf. A023200, A046132, A172494, A174370, A176130, A178228, A176229.
%K nonn
%O 1,1
%A Ulrich Krug (leuchtfeuer37(AT)gmx.de), May 23 2010
%E Corrected by _D. S. McNeil_, Nov 24 2010
%E More terms from _Amiram Eldar_, Dec 24 2019
|
