A138940 - OEIS

%I #62 Sep 10 2024 16:14:21

%S 2,4,10,12,14,19,23,24,36,38,39,48,62,93,106,120,134,150,196,317,320,

%T 385,586,597,654,738,945,1031,1172,1282,1404,1426,1452,1521,1752,1812,

%U 1836,1844,1862,2134,2232,2264,2667,3750,3903,3927,4274,4354,5877,6022

%N Indices n such that A019328(n) = Phi(n,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 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

%H Ray Chandler, <a href="/A138940/b138940.txt">Table of n, a(n) for n = 1..102</a> (first 50 terms from Robert Price, terms 92-93 from Serge Batalov, others from Kamada link)

%H Chris Caldwell, <a href="https://t5k.org/glossary/page.php?sort=UniquePrime">Unique Primes</a>.

%H Makoto Kamada, <a href="https://stdkmd.net/nrr/repunit/phin10.htm">Factorizations of Phi_n(10)</a> (including prime members up to 200000).

%H <a href="/index/Cy#CyclotomicPolynomialsValuesAtX">Index entries for cyclotomic polynomials, values at X</a>

%t Select[Range[1000], PrimeQ[Cyclotomic[#, 10]] &] (* _T. D. Noe_, Mar 03 2012 *)

%o (PARI) for( i=1,999, isprime( polcyclo(i,10)) && print1( i","))

%Y Cf. A019328, A040017, A085035, A252491.

%Y Cf. Subsequence of A007498, contains A004023.

%K nonn

%O 1,1

%A _M. F. Hasler_, Apr 03 2008

%E a(28)-a(43) from _Robert Price_, Mar 03 2012

%E a(44)-a(50) from _Robert Price_, Apr 14 2012

%E a(51)-a(91) from _Ray Chandler_, Maksym Voznyy et al. (cf. Phi_n(10) link), ca. 2009

%E a(92)-a(93) from _Serge Batalov_, Mar 28 2015