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A214676 A(n,k) is n represented in bijective base-k numeration; square array A(n,k), n>=1, k>=1, read by antidiagonals. 8
1, 1, 11, 1, 2, 111, 1, 2, 11, 1111, 1, 2, 3, 12, 11111, 1, 2, 3, 11, 21, 111111, 1, 2, 3, 4, 12, 22, 1111111, 1, 2, 3, 4, 11, 13, 111, 11111111, 1, 2, 3, 4, 5, 12, 21, 112, 111111111, 1, 2, 3, 4, 5, 11, 13, 22, 121, 1111111111 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

The digit set for bijective base-k numeration is {1, 2, ..., k}.

LINKS

Alois P. Heinz, Antidiagonals n = 1..18, flattened

R. R. Forslund, A logical alternative to the existing positional number system, Southwest Journal of Pure and Applied Mathematics, Vol. 1, 1995, 27-29.

Eric Weisstein's World of Mathematics, Zerofree

Wikipedia, Bijective numeration

EXAMPLE

Square array A(n,k) begins:

:         1,   1,  1,  1,  1,  1,  1,  1, ...

:        11,   2,  2,  2,  2,  2,  2,  2, ...

:       111,  11,  3,  3,  3,  3,  3,  3, ...

:      1111,  12, 11,  4,  4,  4,  4,  4, ...

:     11111,  21, 12, 11,  5,  5,  5,  5, ...

:    111111,  22, 13, 12, 11,  6,  6,  6, ...

:   1111111, 111, 21, 13, 12, 11,  7,  7, ...

:  11111111, 112, 22, 14, 13, 12, 11,  8, ...

MAPLE

A:= proc(n, b) local d, l, m; m:= n; l:= NULL;

      while m>0 do  d:= irem(m, b, 'm');

        if d=0 then d:=b; m:=m-1 fi;

        l:= d, l

      od; parse(cat(l))

    end:

seq(seq(A(n, 1+d-n), n=1..d), d=1..12);

MATHEMATICA

A[n_, b_] := Module[{d, l, m}, m = n; l = Nothing; While[m > 0, {m, d} = QuotientRemainder[m, b]; If[d == 0, d = b; m--]; l = {d, l}]; FromDigits @ Flatten @ l];

Table[A[n, d-n+1], {d, 1, 12}, {n, 1, d}] // Flatten (* Jean-Fran├žois Alcover, May 28 2019, from Maple *)

CROSSREFS

Columns k=1-9 give: A000042, A007931, A007932, A084544, A084545, A057436, A214677, A214678, A052382.

Sequence in context: A010196 A039617 A229186 * A010198 A307245 A204846

Adjacent sequences:  A214673 A214674 A214675 * A214677 A214678 A214679

KEYWORD

nonn,tabl

AUTHOR

Alois P. Heinz, Jul 25 2012

STATUS

approved

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Last modified June 19 13:11 EDT 2019. Contains 324222 sequences. (Running on oeis4.)