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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 Cuculière, 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.)