A214326 Square array read by antidiagonals in which T(n,b) gives the n-th Fibonacci number written in base b with n,b >= 1.

1, 1, 1, 1, 1, 11, 1, 1, 10, 111, 1, 1, 2, 11, 11111, 1, 1, 2, 10, 101, 11111111, 1, 1, 2, 3, 12, 1000, 1111111111111, 1, 1, 2, 3, 11, 22, 1101, 111111111111111111111, 1, 1, 2, 3, 10, 20, 111, 10101, 1111111111111111111111111111111111, 1, 1, 2, 3, 5, 13, 31, 210, 100010

Offset: 1

Author

Alois P. Heinz, Jul 24 2012

Keywords

• nonn
• tabl
• easy
• base

Comments

For b > 10, some terms cannot be properly notated using only decimal characters.

Examples

			Square array A(n,b) begins:
              1,    1,   1,  1,  1,  1,  1,  1,  1,  1,  1,  1, ...
              1,    1,   1,  1,  1,  1,  1,  1,  1,  1,  1,  1, ...
             11,   10,   2,  2,  2,  2,  2,  2,  2,  2,  2,  2, ...
            111,   11,  10,  3,  3,  3,  3,  3,  3,  3,  3,  3, ...
          11111,  101,  12, 11, 10,  5,  5,  5,  5,  5,  5,  5, ...
       11111111, 1000,  22, 20, 13, 12, 11, 10,  8,  8,  8,  8, ...
  1111111111111, 1101, 111, 31, 23, 21, 16, 15, 14, 13, 12, 11, ...
		

Links

• Alois P. Heinz, Antidiagonals n = 1..13

Crossrefs

Columns b=1-10, 12, 13 give: A108047, A004685, A004686, A004687, A004688, A004689, A004690, A004691, A004692, A000045, A004693, A004694.

Cf. A037842, A131293.

Programs

Maple

A:= proc(n, b) local f, l; f:= combinat[fibonacci](n);
      if b=1 then parse(cat(1$f))
    else l:= NULL;
         while f>0 do l:= irem(f, b, 'f'), l od;
         parse(cat(l))
      fi
    end:
seq(seq(A(n, 1+d-n), n=1..d), d=1..10);