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A293654
Integers not represented by cyclotomic binary forms.
14
1, 2, 6, 14, 15, 22, 23, 24, 30, 33, 35, 38, 42, 44, 46, 47, 51, 54, 56, 59, 60, 62, 66, 69, 70, 71, 77, 78, 83, 86, 87, 88, 92, 94, 95, 96, 99, 102, 105, 107, 110, 114, 115, 118, 119, 120, 123, 126, 131, 132, 134, 135, 138, 140, 141, 142, 143, 150
OFFSET
1,2
LINKS
Étienne Fouvry, Claude Levesque, Michel Waldschmidt, Representation of integers by cyclotomic binary forms, arXiv:1712.09019 [math.NT], 2017.
MAPLE
g := 1;
for m from 1 to 1000 do
for n from 3 to 50 do
for x from -50 to 50 do
for y from -50 to 50 do
if (F[n] = m, max(abs(x), abs(y)) > 1
then r[g] := m; m := m+1; n := 3;
x := -50; y := -50; g := g+1
fi;
od; od; od; od;
for t to 519 do print(r[{t}] = r[t]) od;
s[1] := 1; s[2] := 2; g := 2;
for i from 1 to 518 do
for j from r[i]+1 to r[i+1]-1 do
g := g+1; s[g] := j
od; od;
for t to 481 do s[t] od;
MATHEMATICA
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]];
Select[Range[150], !isA296095[#]&] (* Jean-François Alcover, Jun 21 2018, after Peter Luschny *)
PROG
(Sage)
def A293654list(upto):
return [n for n in (1..upto) if not isA296095(n)]
print(A293654list(150)) # Peter Luschny, Feb 25 2018
CROSSREFS
Complement of A296095.
Sequence in context: A263691 A160657 A222087 * A128660 A212719 A145213
KEYWORD
nonn
AUTHOR
Michel Waldschmidt, Feb 16 2018
STATUS
approved