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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.
14
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
OFFSET
1,3
COMMENTS
The digit set for bijective base-k numeration is {1, 2, ..., k}.
LINKS
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
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
A(n+1,n) gives A010850.
Sequence in context: A010196 A039617 A229186 * A010198 A307245 A204846
KEYWORD
nonn,tabl
AUTHOR
Alois P. Heinz, Jul 25 2012
STATUS
approved