login
Indices k such that A019321(k)=Phi[k](3) is prime, where Phi is a cyclotomic polynomial.
4

%I #21 Sep 10 2024 16:14:13

%S 1,3,6,7,9,10,12,13,14,15,21,24,26,33,36,40,46,60,63,70,71,72,86,103,

%T 108,130,132,143,145,154,161,236,255,261,276,279,287,304,364,430,464,

%U 513,528,541,562,665,672,680,707,718,747,760,782,828,875,892,974,984

%N Indices k such that A019321(k)=Phi[k](3) is prime, where Phi is a cyclotomic polynomial.

%H Robert Price, <a href="/A138933/b138933.txt">Table of n, a(n) for n = 1..167</a>

%H Yves Gallot, <a href="http://yves.gallot.pagesperso-orange.fr/papers/cyclotomic.html">Cyclotomic polynomials and prime numbers</a>

%H <a href="/index/Cy#CyclotomicPolynomialsValuesAtX">Index entries for cyclotomic polynomials, values at X</a>

%t Select[Range[1000], PrimeQ[Cyclotomic[#, 3]] &]

%o (PARI) for( i=1,999, ispseudoprime( polcyclo(i,3)) && print1( i","))

%Y Cf. A019321, A072226, A138920-A138940.

%K nonn

%O 1,2

%A _M. F. Hasler_, Apr 03 2008