|
%I #25 Jan 16 2019 16:40:13
%S 1,1,2,1,2,1,16,3,2,1,32,1,118,417,2,1,14,1,22,81,76,1,12,55,28,15,0,
%T 1,110,1,232,117,230,3,12,1,4,375,2,1,48,1,46,15,218,1,78,7,100,993,
%U 28,1,624,13,252,183,226,1,104,1,1348,777,1294,0,1806,1,306,1815,10,1,30,1
%N Least k >= 1 such that k^n + n is prime, or 0 if no such k exists.
%C Because the polynomial x^n + n is reducible for n in A097792, a(27) and a(64) are 0. Although x^4 + 4 is reducible, the factor x^2 - 2x + 2 is 1 for x=1. - _T. D. Noe_, Aug 24 2004
%H Hugo Pfoertner, <a href="/A072883/b072883.txt">Table of n, a(n) for n = 1..756</a>
%t Table[If[MemberQ[{27, 64}, n], 0, k=1; While[ !PrimeQ[k^n+n], k++ ]; k], {n, 100}]
%t (* Second program: *)
%t okQ[n_] := n == 4 || IrreduciblePolynomialQ[x^n + n];
%t a[n_] := If[!okQ[n], 0, s = 1; While[!PrimeQ[s^n + n], s++]; s];
%t Table[a[n], {n, 1, 100}] (* _Jean-François Alcover_, Jan 15 2019, from PARI *)
%o (PARI) isok(n) = (n==4) || polisirreducible(x^n+n);
%o a(n) = if (!isok(n), 0, my(s=1); while(!isprime(s^n+n), s++); s); \\ adapted by _Michel Marcus_, Jan 15 2019
%Y Cf. A097792 (n such that x^n + n is reducible).
%Y Cf. A239666, A303121, A303122.
%K nonn
%O 1,3
%A _Benoit Cloitre_, Aug 13 2002
%E More terms from _T. D. Noe_, Aug 24 2004
|
