|
%I #20 Oct 13 2019 23:52:10
%S 2,2,3,2,5,3,7,2,3,11,11,13,13,43,151,2,17,46441,19,61681,368089,683,
%T 23,241,5,2731,3,15790321,29,331,31,2,599479,43691,
%U 2984619585279628795345143571,530713,37,174763,900900900900990990990991,61681,41,5419,43,9080418348371887359375390001
%N a(n) is the first prime value of the n-th cyclotomic polynomial.
%H Robert Israel, <a href="/A307687/b307687.txt">Table of n, a(n) for n = 1..426</a>
%F a(p^k) = p if p is prime.
%F a(n) == 1 (mod A117544(n)) for n >= 2.
%F a(n) = Phi(n,A117544(n)) where Phi(n,k) is the n-th cyclotomic polynomial evaluated at k.
%e a(10)=11 because the 10th cyclotomic polynomial is Phi(10,x) = x^4 - x^3 + x^2 - x + 1, and Phi(10,2)=11 is prime but Phi(10,1)=1 is not prime.
%p f:= proc(n) local C,x,k;
%p C:= unapply(numtheory:-cyclotomic(n,x),x);
%p for k from 1 do if isprime(C(k)) then return C(k) fi od
%p end proc:
%p map(f, [$1..100]);
%t a[n_] := Module[{c, k}, c[x_] = Cyclotomic[n, x]; For[k = 1, True, k++, If[PrimeQ[c[k]], Return[c[k]]]]]; Array[a, 100] (* _Jean-François Alcover_, Apr 29 2019 *)
%o (PARI) a(n) = my(k=1, p); while (!isprime(p=polcyclo(n, k)), k++); p; \\ _Michel Marcus_, Apr 22 2019
%Y Cf. A117544.
%K nonn
%O 1,1
%A _Robert Israel_, Apr 22 2019
|
