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%I A193366 #39 Jul 30 2017 14:50:23
%S A193366 5,22621,245411,346201,637421,837931,2625641,3835261,6377551,15018571,
%T A193366 16007041,21700501,30397351,35615581,52822061,78914411,97039801,
%U A193366 147753211,189004141,195534851,209102521,223364311,279086341,324842131,421106401,445120421,566124791,693025471,727832821,745720141,880331261,943280801,987082981,1544755411,1740422941
%N A193366 Primes of the form n^4 + n^3 + n^2 + n + 1 where n is nonprime.
%C A193366 Note that there are no primes of the form n^3 + n^2 + n + 1 = (n+1)*(n^2+1) as irreducible components over Z.
%C A193366 From _Bernard Schott_, May 15 2017: (Start)
%C A193366 These are the primes associated with A286094.
%C A193366 A088548 = A190527 Union {This sequence}.
%C A193366 All the numbers of this sequence n^4 + n^3 + n^2 + n + 1 = 11111_n with n > 1 are Brazilian numbers, so belong to A125134 and A085104. (End)
%H A193366 Vincenzo Librandi, <a href="/A193366/b193366.txt">Table of n, a(n) for n = 1..1000</a>
%H A193366 Bernard Schott, <a href="/A125134/a125134.pdf">Les nombres brésiliens</a>, Reprinted from Quadrature, no. 76, avril-juin 2010, pages 30-38.
%F A193366 {n^4 + n^3 + n^2 + n + 1 where n is in A018252}.
%e A193366 a(1) = 1^4 + 1^3 + 1^2 + 1 + 1 = 5.
%e A193366 a(2) = 12^4 + 12^3 + 12^2 + 12 + 1 = 22621.
%p A193366 for n from 1 to 150 do p(n):= 1+n+n^2+n^3+n^4;
%p A193366 if tau(n)>2 and isprime(p(n)) then print(n,p(n)) else fi od: # _Bernard Schott_, May 15 2017
%t A193366 Select[Map[Total[#^Range[0, 4]] &, Select[Range@ 204, ! PrimeQ@ # &]], PrimeQ] (* _Michael De Vlieger_, May 15 2017 *)
%o A193366 (PARI) print1(5);forcomposite(n=4,1e3,if(isprime(t=n^4+n^3+n^2+n+1),print1(", "t))) \\ _Charles R Greathouse IV_, Mar 25 2013
%Y A193366 Subsequence of A088548.
%Y A193366 Cf. A000040, A018252, A185632, A192321.
%Y A193366 Cf. A049409, A053699, A065509, A085104, A088548, A125134, A190527, A286094.
%K A193366 nonn,easy
%O A193366 1,1
%A A193366 _Jonathan Vos Post_, Dec 20 2012

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