A293654 Integers not represented by cyclotomic binary forms.
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
Keywords
Links
- Michel Waldschmidt, Table of n, a(n) for n = 1..249
- Étienne Fouvry, Claude Levesque, and Michel Waldschmidt, Representation of integers by cyclotomic binary forms, arXiv:1712.09019 [math.NT], 2017.
Crossrefs
Programs
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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 *)
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Sage
def A293654list(upto): return [n for n in (1..upto) if not isA296095(n)] print(A293654list(150)) # Peter Luschny, Feb 25 2018
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