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A022423 Kim-sums: "Kimberling sums" K_n + K_12. 6
11, 31, 34, 36, 39, 42, 44, 47, 49, 52, 55, 57, 60, 63, 65, 68, 70, 73, 76, 78, 81, 83, 86, 89, 91, 94, 97, 99, 102, 104, 107, 110, 112, 115, 118, 120, 123, 125, 128, 131, 133, 136, 138, 141, 144, 146, 149, 152, 154, 157, 159, 162, 165, 167, 170, 172, 175, 178, 180 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

REFERENCES

Posting to math-fun mailing list Jan 10 1997.

LINKS

Table of n, a(n) for n=0..58.

J. H. Conway, Allan Wechsler, Marc LeBrun, Dan Hoey, N. J. A. Sloane, On Kimberling Sums and Para-Fibonacci Sequences, Correspondence and Postings to Math-Fun Mailing List, Nov 1996 to Jan 1997

MAPLE

Ki := proc(n, i)

    option remember;

    local phi ;

    phi := (1+sqrt(5))/2 ;

    if i= 0 then

        n;

    elif i=1 then

        floor((n+1)*phi) ;

    else

        procname(n, i-1)+procname(n, i-2) ;

    end if;

end proc:

Kisum := proc(n, m)

    local ks, a, i;

    ks := [seq( Ki(n, i)+Ki(m, i), i=0..5)] ;

    for i from 0 to 2 do

        for a from 0 do

            if Ki(a, 0) = ks[i+1] and Ki(a, 1) = ks[i+2] then

                return a;

            end if;

            if Ki(a, 0) > ks[i+1] then

                break;

            end if;

        end do:

    end do:

end proc:

A022423 := proc(n)

    if n = 0 then

        11;

    else

        Kisum(n-1, 11) ;

    end if;

end proc:

seq(A022423(n), n=0..80) ; # R. J. Mathar, Sep 03 2016

MATHEMATICA

Ki[n_, i_] := Ki[n, i] = Module[{phi = (1 + Sqrt[5])/2}, If[i == 0, n, If[i == 1, Floor[(n+1)*phi], Ki[n, i-1] + Ki[n, i-2]]]];

Kisum[n_, m_] := Module[{ks, a, i}, ks = Table[Ki[n, i] + Ki[m, i], {i, 0, 5}]; For[i = 0, i <= 2, i++, For[a = 0, True, a++, If[Ki[a, 0] == ks[[i+1]] && Ki[a, 1] == ks[[i+2]], Return[a]]; If[Ki[a, 0] > ks[[i+1]], Break[]]]]];

a[n_] := If[n == 0, 11, Kisum[n-1, 11]];

a /@ Range[0, 58] (* Jean-Fran├žois Alcover, Mar 29 2020, after R. J. Mathar *)

CROSSREFS

The "Kim-sums" K_n + K_i for i = 2 through 12 are given in A022413, A022414, A022415, A022416, ..., A022423.

Sequence in context: A250468 A259515 A183845 * A173972 A167488 A298566

Adjacent sequences:  A022420 A022421 A022422 * A022424 A022425 A022426

KEYWORD

nonn

AUTHOR

Marc LeBrun

STATUS

approved

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Last modified September 20 10:24 EDT 2020. Contains 337264 sequences. (Running on oeis4.)