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%I #48 Apr 06 2024 15:00:46
%S 1,2,6,14,15,22,23,24,30,33,35,38,42,44,46,47,51,54,56,59,60,62,66,69,
%T 70,71,77,78,83,86,87,88,92,94,95,96,99,102,105,107,110,114,115,118,
%U 119,120,123,126,131,132,134,135,138,140,141,142,143,150
%N Integers not represented by cyclotomic binary forms.
%H Michel Waldschmidt, <a href="/A293654/b293654.txt">Table of n, a(n) for n = 1..249</a>
%H Étienne Fouvry, Claude Levesque, Michel Waldschmidt, <a href="https://arxiv.org/abs/1712.09019">Representation of integers by cyclotomic binary forms</a>, arXiv:1712.09019 [math.NT], 2017.
%p g := 1;
%p for m from 1 to 1000 do
%p for n from 3 to 50 do
%p for x from -50 to 50 do
%p for y from -50 to 50 do
%p if (F[n] = m, max(abs(x), abs(y)) > 1
%p then r[g] := m; m := m+1; n := 3;
%p x := -50; y := -50; g := g+1
%p fi;
%p od; od; od; od;
%p for t to 519 do print(r[{t}] = r[t]) od;
%p s[1] := 1; s[2] := 2; g := 2;
%p for i from 1 to 518 do
%p for j from r[i]+1 to r[i+1]-1 do
%p g := g+1; s[g] := j
%p od; od;
%p for t to 481 do s[t] od;
%t isA296095[n_] := If[n<3, Return[False], logn = Log[n]^1.161; K = Floor[ 5.383*logn]; M = Floor[2*(n/3)^(1/2)]; k = 3; While[True, If[k == 7, K = Ceiling[4.864*logn]; M = Ceiling[2*(n/11)^(1/4)]]; For[y = 2, y <= M, y++, p[z_] = y^EulerPhi[k]*Cyclotomic[k, z]; For[x = 1, x <= y, x++, If[n == p[x/y], Return[True]]]]; k++; If[k>K, Break[]]]; Return[False]];
%t Select[Range[150], !isA296095[#]&] (* _Jean-François Alcover_, Jun 21 2018, after _Peter Luschny_ *)
%o (Sage)
%o def A293654list(upto):
%o return [n for n in (1..upto) if not isA296095(n)]
%o print(A293654list(150)) # _Peter Luschny_, Feb 25 2018
%Y Complement of A296095.
%K nonn
%O 1,2
%A _Michel Waldschmidt_, Feb 16 2018
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