login
Indices n such that A020501(n) = phi(n)(-2) is prime, where Phi is a cyclotomic polynomial.
2

%I #20 Nov 11 2019 10:25:58

%S 3,4,5,6,7,8,10,11,12,13,14,15,16,17,18,19,21,23,24,26,30,31,32,34,38,

%T 39,40,43,45,49,54,56,61,62,63,66,75,79,80,85,87,98,101,117,120,122,

%U 127,130,138,154,161,167,170,178,183,184,186,187,191,192,199,205,207,208

%N Indices n such that A020501(n) = phi(n)(-2) is prime, where Phi is a cyclotomic polynomial.

%C While the sequence is not very interesting up to a(n)<300, there are only 4 values in the interval [400,599].

%H Robert Price, <a href="/A138928/b138928.txt">Table of n, a(n) for n = 1..227</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[3, 1000], PrimeQ[ Cyclotomic[#, -2]] &] (* _Robert G. Wilson v_, Mar 25 2012 *)

%o (PARI) for( i=1,999, isprime( polcyclo(i,-2)) && print1( i",")) /* for PARI < 2.4.2 use ...subst(polcyclo(i),x,-2)...*/

%Y Cf. A020501, A138920-A138940.

%K nonn

%O 1,1

%A _M. F. Hasler_, Apr 03 2008