A325870 - OEIS

%I #17 Apr 06 2024 14:59:17

%S 11,13,17,31,43,61,73,97,127,151,181,193,211,241,257,331,337,421,461,

%T 463,521,541,547,577,601,641,683,757,881,991,1009,1021,1031,1093,1297,

%U 1621,1801,1871,1873,1933,2221,2417,2657,2731,2801,3001,3121,3361,3571,3697

%N Primes represented by non-quadratic cyclotomic binary forms.

%H Peter Luschny, <a href="/A325870/b325870.txt">Table of n, a(n) for n = 1..185</a>

%H Étienne Fouvry, Claude Levesque, and Michel Waldschmidt, <a href="http://arxiv.org/abs/1712.09019">Representation of integers by cyclotomic binary forms</a>, arXiv:1712.09019 [math.NT], 2017 and <a href="https://doi.org/10.4064/aa171012-24-12">Acta Arithmetica</a>, online 15 March 2018.

%o (PARI)

%o isA325870(n) =

%o {

%o     my(K, M, phi);

%o     K = floor(5.383*log(n)^1.161);

%o     M = floor(2*sqrt(n/3));

%o     for(k = 3, K,

%o         phi = eulerphi(k);

%o         if(phi >= 4,

%o             for(y = 1, M,

%o                 for(x = y + 1, M,

%o                     if(n == y^phi*polcyclo(k, x/y),

%o                         return(1)

%o     )))));

%o     return(0)

%o }

%Y Cf. A296095, A293654, A325143, A325145.

%K nonn

%O 1,1

%A _Peter Luschny_, May 26 2019

%E At the suggestion of _Michel Waldschmidt_