A325870 Primes represented by non-quadratic cyclotomic binary forms.

11, 13, 17, 31, 43, 61, 73, 97, 127, 151, 181, 193, 211, 241, 257, 331, 337, 421, 461, 463, 521, 541, 547, 577, 601, 641, 683, 757, 881, 991, 1009, 1021, 1031, 1093, 1297, 1621, 1801, 1871, 1873, 1933, 2221, 2417, 2657, 2731, 2801, 3001, 3121, 3361, 3571, 3697

Offset

1,1

Links

Peter Luschny, Table of n, a(n) for n = 1..185

Étienne Fouvry, Claude Levesque, and Michel Waldschmidt, Representation of integers by cyclotomic binary forms, arXiv:1712.09019 [math.NT], 2017 and Acta Arithmetica, online 15 March 2018.

Prog

(PARI)
isA325870(n) =
{
    my(K, M, phi);
    K = floor(5.383*log(n)^1.161);
    M = floor(2*sqrt(n/3));
    for(k = 3, K,
        phi = eulerphi(k);
        if(phi >= 4,
            for(y = 1, M,
                for(x = y + 1, M,
                    if(n == y^phi*polcyclo(k, x/y),
                        return(1)
    )))));
    return(0)
}

Crossrefs

Cf. A296095, A293654, A325143, A325145.

Sequence in context: A240570 A354524 A162237 * A090236 A240623 A240624

Adjacent sequences: A325867 A325868 A325869 * A325871 A325872 A325873

Keyword

nonn

Author

Peter Luschny, May 26 2019

Extensions

At the suggestion of Michel Waldschmidt

Status

approved