A325143 -id:A325143 - cp's OEIS frontend

A325145 Primes not representable by cyclotomic binary forms.

2, 23, 47, 59, 71, 83, 107, 131, 167, 179, 191, 227, 239, 251, 263, 311, 347, 359, 383, 419, 431, 443, 467, 479, 491, 503, 563, 587, 599, 647, 659, 719, 743, 827, 839, 863, 887, 911, 947, 971, 983, 1019, 1091, 1103, 1151, 1163, 1187, 1223

Offset: 1

Peter Luschny, May 16 2019

nonn

Étienne Fouvry, Claude Levesque, Michel Waldschmidt, Representation of integers by cyclotomic binary forms, Acta Arithmetica 184 (2018), 67-86; arXiv:1712.09019, arXiv:1712.09019 [math.NT], 2017.

A325143 gives the primes represented by cyclotomic binary forms.

Cf. A293654, A299214, A299498, A299733, A299928, A299930, A299956, A299964.

[n for n in 1:1223 if isprime(ZZ(n)) && ! isA325143(n)] |> println

A325141 Number of primes represented by cyclotomic binary forms < 10000*n.

Original entry on oeis.org

925, 1700, 2435, 3147, 3848, 4538, 5189, 5875, 6537, 7201, 7843, 8475, 9112, 9749, 10391

Offset: 1

Peter Luschny, May 20 2019

Empirically approximated by (3/4)*x/(log(x) - 1).

Cf. A325143.

A325870 Primes represented by non-quadratic cyclotomic binary forms.

Original entry on oeis.org

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

Peter Luschny, May 26 2019

nonn

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.

Cf. A296095, A293654, A325143, A325145.

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)
}

At the suggestion of Michel Waldschmidt

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A325145 Primes not representable by cyclotomic binary forms.

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A325141 Number of primes represented by cyclotomic binary forms < 10000*n.

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A325870 Primes represented by non-quadratic cyclotomic binary forms.

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