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A057854
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Non-Lucas numbers: the complement of A000032.
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7
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5, 6, 8, 9, 10, 12, 13, 14, 15, 16, 17, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 77, 78, 79, 80
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OFFSET
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1,1
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COMMENTS
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The formula is a consequence of the Lambek-Moser theorem.
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LINKS
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FORMULA
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a(n) = floor(1/2 - LambertW(-1, -log(phi)/phi^(n+1/2))/log(phi)) with phi = (1+sqrt(5))/2. - Nicolas Normand (nicolas.normand (at) polytech.univ-nantes.fr)
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MAPLE
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a := proc(n) floor(-1/ln(1/2+1/2*5^(1/2))*LambertW(-1, -ln(1/2+1/2*5^(1/2))/ ((1/2+1/2*5^(1/2))^(n+1/2)))+1/2) end; # Simon Plouffe, Nov 30 2017
# alternative
isA000032 := proc(n)
local l1, l2 ;
if n <= 0 then
false;
elif n <= 4 then
true ;
else
l1 := 3 ; l2 := 4 ;
while true do
l := l1+l2 ;
if l > n then
return false;
elif l = n then
return true;
else
l1 := l2 ; l2 := l ;
end if;
end do:
end if;
end proc:
isA057854 := proc(n)
not isA000032(n) ;
end proc:
option remember;
if n = 1 then
5 ;
else
for a from procname(n-1)+1 do
if isA057854(a) then
return a;
end if;
end do:
end if;
end proc:
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MATHEMATICA
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a[n_] := With[{phi = (1 + Sqrt[5])/2}, Floor[1/2 - LambertW[-1, -Log[phi]/phi^(n + 1/2)]/Log[phi]]];
b:= Complement[Range[1, 100], LucasL[Range[20]]]; Table[b[[n+1]], {n, 1, 70}] (* G. C. Greubel, Jun 19 2019 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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More terms from Larry Reeves (larryr(AT)acm.org), Nov 28 2000
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STATUS
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approved
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