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 A057854 Non-Lucas numbers: the complement of A000032. 6
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The formula is a consequence of the Lambek-Moser theorem. LINKS G. C. Greubel, Table of n, a(n) for n = 1..10000 Wikipedia, Lambek-Moser theorem 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 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 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 *) CROSSREFS Sequence in context: A201512 A242290 A296562 * A033266 A102408 A240564 Adjacent sequences:  A057851 A057852 A057853 * A057855 A057856 A057857 KEYWORD nonn,easy AUTHOR Roger CuculiÃ¨re, Nov 12 2000 EXTENSIONS More terms from Larry Reeves (larryr(AT)acm.org), Nov 28 2000 STATUS approved

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Last modified February 25 12:01 EST 2020. Contains 332233 sequences. (Running on oeis4.)