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%I #26 Feb 14 2020 10:05:27
%S 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,
%T 12,22,1111111,1,2,3,4,11,13,111,11111111,1,2,3,4,5,12,21,112,
%U 111111111,1,2,3,4,5,11,13,22,121,1111111111
%N A(n,k) is n represented in bijective base-k numeration; square array A(n,k), n>=1, k>=1, read by antidiagonals.
%C The digit set for bijective base-k numeration is {1, 2, ..., k}.
%H Alois P. Heinz, <a href="/A214676/b214676.txt">Antidiagonals n = 1..18, flattened</a>
%H R. R. Forslund, <a href="http://www.emis.de/journals/SWJPAM/Vol1_1995/rrf01.ps">A logical alternative to the existing positional number system</a>, Southwest Journal of Pure and Applied Mathematics, Vol. 1, 1995, 27-29.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Zerofree.html">Zerofree</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Bijective_numeration">Bijective numeration</a>
%e Square array A(n,k) begins:
%e : 1, 1, 1, 1, 1, 1, 1, 1, ...
%e : 11, 2, 2, 2, 2, 2, 2, 2, ...
%e : 111, 11, 3, 3, 3, 3, 3, 3, ...
%e : 1111, 12, 11, 4, 4, 4, 4, 4, ...
%e : 11111, 21, 12, 11, 5, 5, 5, 5, ...
%e : 111111, 22, 13, 12, 11, 6, 6, 6, ...
%e : 1111111, 111, 21, 13, 12, 11, 7, 7, ...
%e : 11111111, 112, 22, 14, 13, 12, 11, 8, ...
%p A:= proc(n, b) local d, l, m; m:= n; l:= NULL;
%p while m>0 do d:= irem(m, b, 'm');
%p if d=0 then d:=b; m:=m-1 fi;
%p l:= d, l
%p od; parse(cat(l))
%p end:
%p seq(seq(A(n, 1+d-n), n=1..d), d=1..12);
%t 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];
%t Table[A[n, d-n+1], {d, 1, 12}, {n, 1, d}] // Flatten (* _Jean-François Alcover_, May 28 2019, from Maple *)
%Y Columns k=1-9 give: A000042, A007931, A007932, A084544, A084545, A057436, A214677, A214678, A052382.
%Y A(n+1,n) gives A010850.
%K nonn,tabl
%O 1,3
%A _Alois P. Heinz_, Jul 25 2012
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