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A138926 Indices k such that A020503(k)=Phi[k](-4) is prime, where Phi is a cyclotomic polynomial.

%I A138926 #27 Jan 17 2020 01:21:54
%S A138926 3,4,8,12,16,20,28,40,60,92,96,104,140,148,156,300,356,408,596,612,
%T A138926 692,732,756,800,952,996,1004,1228,1268,2240,2532,3060,3796,3824,3944,
%U A138926 5096,5540,7476,7700,8544,9800,14628,15828,16908,18480,20260,21924,24656,38456
%N A138926 Indices k such that A020503(k)=Phi[k](-4) is prime, where Phi is a cyclotomic polynomial.
%C A138926 It appears that for all k>1, a(k) is a multiple of 4.
%C A138926 It also appears that all Cyclotomic Polynomials, Phi[k](x), where k is a multiple of 4 have no odd powers of x.  For example, Phi[20](x)=x^8-x^6+x^4-x^2+1.  This implies that Phi[k](x)=Phi[k](-x), where k is a multiple of 4. - _Robert Price_, Apr 14 2012
%H A138926 Robert Price, <a href="/A138926/b138926.txt">Table of n, a(n) for n = 1..49</a>
%H A138926 Yves Gallot, <a href="http://yves.gallot.pagesperso-orange.fr/papers/cyclotomic.html">Cyclotomic polynomials and prime numbers</a>
%t A138926 Select[ Range[3, 5000], PrimeQ[ Cyclotomic[#, -4]] &] (* _Robert G. Wilson v_, Mar 25 2012 *)
%o A138926 (PARI) for( i=1,999, ispseudoprime( polcyclo(i,-4)) && print1( i",")) /* use ...subst(polcyclo(i),x,-4)... in PARI < 2.4.2 */
%Y A138926 Cf. A020503, A138920-A138940.
%K A138926 nonn
%O A138926 1,1
%A A138926 _M. F. Hasler_, Apr 03 2008
%E A138926 a(36)-a(49) from _Robert Price_, Apr 07 2012