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

Author

M. F. Hasler, Apr 03 2008

Keywords

• nonn

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

Crossrefs

Cf. A019328, A040017, A138940.

Programs

Mathematica

Select[Range[1000], PrimeQ[Cyclotomic[#, -10]] &]

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)... */

Extensions

a(28)-a(43) from Robert Price, Mar 09 2012

a(44)-a(50) from Robert Price, Apr 14 2012