A214326 - OEIS

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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.

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 July 23 06:43 EDT 2017. Contains 289686 sequences.