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%I #37 Mar 12 2018 17:47:27
%S 1,2,7,12,13,17,22,23,24,28,29,30,40,43,44,50,62,63,68,73,74,77,79,83,
%T 85,94,99,110,117,118,120,122,127,129,134,143,145,154,162,164,165,172,
%U 175,177,193,198,204,208,222,227,239,249,254,255,260
%N Numbers n such that n^4 + n^3 + n^2 + n + 1 is prime.
%C There is no square > 1 in this sequence, because if f(n) = n^4 + n^3 + n^2 + n + 1, then f(n^2) = f(n)*f(-n). Actually, f(x) divides f(x^m) for all m not in 5Z. So the only perfect powers in this sequence can be 5th, 25th, 125th... powers. The least perfect power > 1 in this sequence is 22^5. - _M. F. Hasler_, Feb 09 2012
%C The corresponding prime numbers n^4 + n^3 + n^2 + n + 1 are in A088548. - _Bernard Schott_, Dec 19 2012
%C This is also the list of bases where 11111 is a prime number. - _Christian N. K. Anderson_, Mar 28 2013
%H T. D. Noe, <a href="/A049409/b049409.txt">Table of n, a(n) for n = 1..1000</a>
%p A049409:=n->if isprime(n^4+n^3+n^2+n+1) then n fi; seq(A049409(n), n=1..300); # _Wesley Ivan Hurt_, Dec 28 2013
%t lst={}; Do[p=n^0+n^1+n^2+n^3+n^4; If[PrimeQ[p], AppendTo[lst,n]], {n,300}]; lst (* _Vladimir Joseph Stephan Orlovsky_, Jun 10 2009 *)
%t Select[Range[300],PrimeQ[1+Total[#^Range[4]]]&] (* _Harvey P. Dale_, Mar 12 2018 *)
%o (PARI) for(n=1,1000, ispseudoprime(n^4+n^3+n^2+n+1) & print1(n",")) \\ _M. F. Hasler_, Feb 09 2012
%Y Cf. A088548.
%K nonn
%O 1,2
%A _N. J. A. Sloane_
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