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 A214679 T(n,k) = Fibonacci(n) represented in bijective base-k numeration; square array A(n,k), n>=1, k>=1, read by antidiagonals. 10
 1, 1, 1, 1, 1, 11, 1, 1, 2, 111, 1, 1, 2, 11, 11111, 1, 1, 2, 3, 21, 11111111, 1, 1, 2, 3, 12, 112, 1111111111111, 1, 1, 2, 3, 11, 22, 221, 111111111111111111111, 1, 1, 2, 3, 5, 14, 111, 1221, 1111111111111111111111111111111111 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,6 COMMENTS The digit set for bijective base-k numeration is {1, 2, ..., k}. LINKS Alois P. Heinz, Antidiagonals n = 1..13 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 FORMULA T(n,k) = A214676(A000045(n),k). EXAMPLE Square array A(n,k) begins: :                     1,    1,   1,   1,   1,  1,  1,  1,  1, ... :                     1,    1,   1,   1,   1,  1,  1,  1,  1, ... :                    11,    2,   2,   2,   2,  2,  2,  2,  2, ... :                   111,   11,   3,   3,   3,  3,  3,  3,  3, ... :                 11111,   21,  12,  11,   5,  5,  5,  5,  5, ... :              11111111,  112,  22,  14,  13, 12, 11,  8,  8, ... :         1111111111111,  221, 111,  31,  23, 21, 16, 15, 14, ... : 111111111111111111111, 1221, 133, 111,  41, 33, 27, 25, 23, ... MAPLE with(combinat): A:= proc(n, b) local d, l, m; m:= fibonacci(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..10); MATHEMATICA A[n_, b_] := Module[{d, l, m}, m = Fibonacci@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, 10}, {n, 1, d}] // Flatten (* Jean-François Alcover, May 28 2019, from Maple *) CROSSREFS Columns k=1-9 give: A108047, A085652, A282234, A282235, A282236, A282237, A282238, A282239, A282240. Cf. A000045, A214676. Sequence in context: A145140 A010195 A010193 * A332499 A010192 A214326 Adjacent sequences:  A214676 A214677 A214678 * A214680 A214681 A214682 KEYWORD nonn,tabl AUTHOR Alois P. Heinz, Jul 25 2012 STATUS approved

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Last modified August 8 09:16 EDT 2020. Contains 336293 sequences. (Running on oeis4.)