|
%I #10 Mar 29 2017 19:44:18
%S 1,2,9,14,189,204,230,320,680,765,1080,1190,1359,1364,1500,1764,1850,
%T 2049,2115,2360,2379,2919,3050,3110,3179,3579,3794,4164,4215,4470,
%U 5355,5619,5630,5664,5810,5889,5979,6035,6150,6269,6824,6960,7275,8045,8259
%N Numbers n such that n^k+(n+1)^k is prime for k = 1, 2, 4.
%C n^k+(n+1)^k is prime only for k = power of 2.
%C There are 1242 terms < 10^6.
%C All terms > 2 are congruent to 0 or 4 (mod 5). - _Robert Israel_, Mar 29 2017
%H Robert Israel, <a href="/A128780/b128780.txt">Table of n, a(n) for n = 1..10000</a>
%e {2+1, 2^2+3^2,2^4+3^4} = {3,13,97} all prime,
%e {9+10, 9^2+10^2,9^4+10^4} = {19,181,16561} all prime.
%p select(n -> isprime(2*n+1) and isprime(2*n^2+2*n+1) and isprime(n^4+(n+1)^4),
%p [1,2,seq(seq(5*i+j,j=[0,4]),i=1..10000)]); # _Robert Israel_, Mar 29 2017
%t pnQ[n_]:=And@@PrimeQ/@(n^{1,2,4}+(n+1)^{1,2,4}); Select[Range[9000], pnQ] (* _Harvey P. Dale_, Apr 06 2011 *)
%Y Subset of A068501.
%K nonn
%O 1,2
%A _Zak Seidov_, Mar 28 2007
|
