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A138920
Indices k such that A020509(k)=Phi[k](-10) is prime, where Phi is a cyclotomic polynomial.
20
4, 5, 7, 12, 19, 24, 31, 36, 38, 46, 48, 53, 67, 75, 78, 120, 186, 196, 293, 320, 327, 369, 634, 641, 713, 770, 931, 1067, 1172, 1194, 1404, 1452, 1752, 1812, 1836, 1844, 1875, 1890, 2062, 2137, 2177, 2232, 2264, 3011, 3042, 3261, 3341, 4775, 5334, 6685
OFFSET
1,1
COMMENTS
"Unique [period] primes" (A040017) are often of the form Phi[k](10) or Phi[k](-10).
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
LINKS
Ray Chandler, Table of n, a(n) for n = 1..89 (first 76 terms from Robert Price)
C. Caldwell, Unique Primes.
MATHEMATICA
Select[Range[1000], PrimeQ[Cyclotomic[#, -10]] &]
PROG
(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)... */
CROSSREFS
KEYWORD
nonn
AUTHOR
M. F. Hasler, Apr 03 2008
EXTENSIONS
a(28)-a(43) from Robert Price, Mar 09 2012
a(44)-a(50) from Robert Price, Apr 14 2012
STATUS
approved