

A138940


Indices n such that A019328(n) = Phi(n,10) is prime, where Phi is a cyclotomic polynomial.


25



2, 4, 10, 12, 14, 19, 23, 24, 36, 38, 39, 48, 62, 93, 106, 120, 134, 150, 196, 317, 320, 385, 586, 597, 654, 738, 945, 1031, 1172, 1282, 1404, 1426, 1452, 1521, 1752, 1812, 1836, 1844, 1862, 2134, 2232, 2264, 2667, 3750, 3903, 3927, 4274, 4354, 5877, 6022
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OFFSET

1,1


COMMENTS

Unique period primes (A040017) are often of the form Phi(k,10) or Phi(k,10).
Terms of this sequence which are the square of a prime, a(n)=p^2, are such that A252491(p) is prime. Apart from a(2)=2^2, there is no such term up to 26570.  M. F. Hasler, Jan 09 2015


LINKS

Ray Chandler, Table of n, a(n) for n = 1..102 (first 50 terms from Robert Price, terms 9293 from Serge Batalov, others from Kamada link)
Chris Caldwell, Unique Primes.
Makoto Kamada, Factorizations of Phi_n(10) (including prime members up to 200000).
Index entries for cyclotomic polynomials, values at X


MATHEMATICA

Select[Range[1000], PrimeQ[Cyclotomic[#, 10]] &] (* T. D. Noe, Mar 03 2012 *)


PROG

(PARI) for( i=1, 999, isprime( polcyclo(i, 10)) &&& print1( i", ")) /* for PARI < 2.4.2 use ...subst(polcyclo(i, x), x, 10)... */


CROSSREFS

Cf. A019328, A040017, A085035, A252491.
Cf. Subsequence of A007498, contains A004023.
Sequence in context: A249446 A184815 A290473 * A278465 A129412 A266115
Adjacent sequences: A138937 A138938 A138939 * A138941 A138942 A138943


KEYWORD

nonn


AUTHOR

M. F. Hasler, Apr 03 2008


EXTENSIONS

a(28)a(43) from Robert Price, Mar 03 2012
a(44)a(50) from Robert Price, Apr 14 2012
a(51)a(91) from Ray Chandler, Maksym Voznyy et al. (cf. Phi_n(10) link), ca. 2009
a(92)a(93) from Serge Batalov, Mar 28 2015


STATUS

approved



