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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

%I

%S 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,

%T 12,1000,1111111111111,1,1,2,3,11,22,1101,111111111111111111111,1,1,2,

%U 3,10,20,111,10101,1111111111111111111111111111111111,1,1,2,3,5,13,31,210,100010

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

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

%H Alois P. Heinz, <a href="/A214326/b214326.txt">Antidiagonals n = 1..13</a>

%e Square array A(n,b) begins:

%e 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...

%e 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...

%e 11, 10, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, ...

%e 111, 11, 10, 3, 3, 3, 3, 3, 3, 3, 3, 3, ...

%e 11111, 101, 12, 11, 10, 5, 5, 5, 5, 5, 5, 5, ...

%e 11111111, 1000, 22, 20, 13, 12, 11, 10, 8, 8, 8, 8, ...

%e 1111111111111, 1101, 111, 31, 23, 21, 16, 15, 14, 13, 12, 11, ...

%p A:= proc(n, b) local f, l; f:= combinat[fibonacci](n);

%p if b=1 then parse(cat(1$f))

%p else l:= NULL;

%p while f>0 do l:= irem(f, b, 'f'), l od;

%p parse(cat(l))

%p fi

%p end:

%p seq(seq(A(n, 1+d-n), n=1..d), d=1..10);

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

%Y Cf. A037842, A131293.

%K nonn,tabl,easy,base

%O 1,6

%A _Alois P. Heinz_, Jul 24 2012

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Last modified September 18 12:00 EDT 2019. Contains 327170 sequences. (Running on oeis4.)