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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. 2
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,6

COMMENTS

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

LINKS

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

EXAMPLE

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, ...

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);

CROSSREFS

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

Cf. A037842, A131293.

Sequence in context: A010193 A214679 A010192 * A105769 A157171 A143685

Adjacent sequences:  A214323 A214324 A214325 * A214327 A214328 A214329

KEYWORD

nonn,tabl,easy,base

AUTHOR

Alois P. Heinz, Jul 24 2012

STATUS

approved

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Last modified May 23 23:53 EDT 2017. Contains 286937 sequences.