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A269729 a(n) = row number of extended Wythoff array (see A035513) which contains the sequence obtained by reading the n-th row backwards (and adjusting signs). 3
0, 1, 2, 3, 4, 7, 10, 5, 8, 11, 6, 9, 12, 20, 28, 15, 23, 31, 18, 26, 13, 21, 29, 16, 24, 32, 19, 27, 14, 22, 30, 17, 25, 33, 54, 75, 41, 62, 83, 49, 70, 36, 57, 78, 44, 65, 86, 52, 73, 39, 60, 81, 47, 68, 34, 55, 76, 42, 63, 84, 50, 71, 37, 58, 79, 45, 66, 87, 53, 74, 40 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Conjecture: sequence is its own inverse. - R. J. Mathar, May 08 2019

REFERENCES

J. H. Conway, Postings to Math Fun Mailing List, Nov 25 1996 and Dec 02 1996.

LINKS

Table of n, a(n) for n=0..70.

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

EXAMPLE

Take n=5: reading row 5 of A035513 backwards gives ... 23, 14, 9, 5, 4, 1, 3, -2, 5, -7, 12, -19, ..., which after adjusting the signs is row 7, so a(5) = 7.

MAPLE

A035513 := proc(r::integer, c::integer)

    option remember;

    if c = 1 then

        A003622(r) ;

    elif c > 1 then

        A022342(1+procname(r, c-1)) ;

    elif c < 1 then

        procname(r, c+2)-procname(r, c+1) ;

    end if;

end proc:

# search in A035513 for row with consecutive w1, w2

A035513inv := proc(w1::integer, w2::integer)

    local r, c, W1, W2 ;

    for r from 1 do

        if A035513(r, 1) > w2 then

            return -1 ;

        end if;

        for c from 1 do

            W1 := A035513(r, c) ;

            W2 := A035513(r, c+1) ;

            if W1=w1 and W2=w2 then

                return r-1 ;

            elif W2 > w2 then

                break;

            end if;

        end do:

    end do:

end proc:

A269729 := proc(n)

    option remember;

    local c, W1, W2, r, n35513;

    n35513 := n+1 ;

    for c from 1 by -1 do

        W1 := A035513(n35513, c) ;

        W2 := A035513(n35513, c-1) ;

        if W1 < 0 and abs(W2) > abs(W1) then

            r :=  A035513inv(abs(W1), abs(W2)) ;

            if r >= 0 then

                return r;

            end if;

        end if;

    end do:

end proc:

seq(A269729(n), n=0..120) ; # R. J. Mathar, May 08 2019

CROSSREFS

Cf. A000045, A022413-A022423, A035513, A269725, A269726, A269729.

See A269733 for first differences.

Sequence in context: A078696 A256772 A274976 * A098115 A182833 A182832

Adjacent sequences:  A269726 A269727 A269728 * A269730 A269731 A269732

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Mar 08 2016

EXTENSIONS

Terms from a(18) on by R. J. Mathar, May 08 2019

STATUS

approved

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Last modified September 24 03:26 EDT 2021. Contains 347623 sequences. (Running on oeis4.)