A057854 Non-Lucas numbers: the complement of A000032.
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
Offset: 1
Links
- G. C. Greubel, Table of n, a(n) for n = 1..10000
- Wikipedia, Lambek-Moser theorem
Programs
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Maple
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: A057854 := proc(n) 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: seq(A057854(n),n=1..10) ; # R. J. Mathar, Feb 01 2019
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Mathematica
a[n_] := With[{phi = (1 + Sqrt[5])/2}, Floor[1/2 - LambertW[-1, -Log[phi]/phi^(n + 1/2)]/Log[phi]]]; Table[a[n], {n, 1, 70}] (* Peter Luschny, Nov 30 2017 *) b:= Complement[Range[1, 100], LucasL[Range[20]]]; Table[b[[n+1]], {n, 1, 70}] (* G. C. Greubel, Jun 19 2019 *) -
Python
def A057854(n): def f(x): if x<=2: return n+2 a, b, c = 1, 3, 0 while b<=x: a, b = b, a+b c += 1 return n+c+2 m, k = n, f(n) while m != k: m, k = k, f(k) return m # Chai Wah Wu, Sep 10 2024
Formula
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)
a(n) = A090946(n+2). - R. J. Mathar, Jan 29 2019
Extensions
More terms from Larry Reeves (larryr(AT)acm.org), Nov 28 2000
Comments