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-François Alcover, May 28 2019, from Maple *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Alois P. Heinz, Jul 25 2012
STATUS
approved