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%I #26 Apr 03 2023 10:36:11
%S 4,5,7,12,19,24,31,36,38,46,48,53,67,75,78,120,186,196,293,320,327,
%T 369,634,641,713,770,931,1067,1172,1194,1404,1452,1752,1812,1836,1844,
%U 1875,1890,2062,2137,2177,2232,2264,3011,3042,3261,3341,4775,5334,6685
%N Indices k such that A020509(k)=Phi[k](-10) is prime, where Phi is a cyclotomic polynomial.
%C "Unique [period] primes" (A040017) are often of the form Phi[k](10) or Phi[k](-10).
%C Two cyclotomic polynomial identities tightly connect this sequence to A138940: 1) Phi_2k(x) = Phi_k(-x) for odd integer k > 1. 2) Phi_4k(x) = Phi_2k(x^2) for all positive integer k. - _Ray Chandler_, Apr 30 2017
%H Ray Chandler, <a href="/A138920/b138920.txt">Table of n, a(n) for n = 1..89</a> (first 76 terms from Robert Price)
%H C. Caldwell, <a href="https://t5k.org/glossary/page.php?sort=UniquePrime">Unique Primes</a>.
%H <a href="/index/Cy#CyclotomicPolynomialsValuesAtX">Index entries for cyclotomic polynomials, values at X</a>
%t Select[Range[1000], PrimeQ[Cyclotomic[#, -10]] &]
%o (PARI) for( i=1,999, is/*pseudo*/prime( polcyclo(i,-10)) &&& print1( i",")) /* for PARI < 2.4.2 use ...subst(polcyclo(i,x),x,-10)... */
%Y Cf. A019328, A040017, A138940.
%K nonn
%O 1,1
%A _M. F. Hasler_, Apr 03 2008
%E a(28)-a(43) from _Robert Price_, Mar 09 2012
%E a(44)-a(50) from _Robert Price_, Apr 14 2012
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