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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
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
KEYWORD
nonn,tabl,easy,base
AUTHOR
Alois P. Heinz, Jul 24 2012
STATUS
approved