A138920 Indices k such that A020509(k)=Phi[k](-10) is prime, where Phi is a cyclotomic polynomial.

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.

Index entries for cyclotomic polynomials, values at X

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

Cf. A019328, A040017, A138940.

Sequence in context: A160934 A032390 A112918 * A309833 A048224 A064237

Adjacent sequences: A138917 A138918 A138919 * A138921 A138922 A138923

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