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A293654 Integers not represented by cyclotomic binary forms. 11
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Michel Waldschmidt, Table of n, a(n) for n = 1..249

Etienne 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

Adjacent sequences:  A293651 A293652 A293653 * A293655 A293656 A293657

KEYWORD

sign

AUTHOR

Michel Waldschmidt, Feb 16 2018

STATUS

approved

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Last modified January 20 13:11 EST 2019. Contains 319332 sequences. (Running on oeis4.)