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A108731 Triangle read by rows: row n gives digits of n in base factorial. 4
0, 1, 1, 0, 1, 1, 2, 0, 2, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 2, 0, 1, 2, 1, 2, 0, 0, 2, 0, 1, 2, 1, 0, 2, 1, 1, 2, 2, 0, 2, 2, 1, 3, 0, 0, 3, 0, 1, 3, 1, 0, 3, 1, 1, 3, 2, 0, 3, 2, 1, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 2, 0, 1, 0, 2, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,7

COMMENTS

Row lengths are A084558. This sequence contains every finite sequence of nonnegative integers.

T(n,k)=A235168(n,k) for k=0..23; a(n) = A235168(n) for n=0..63, when both tables are seen as flattened lists. - Reinhard Zumkeller, Jan 05 2014

LINKS

Reinhard Zumkeller, Rows n = 0..2000 of triangle, flattened

C. A. Laisant, Sur la numération factorielle, application aux permutations, Bulletin de la Société Mathématique de France, 16 (1888), p. 176-183.

Wikipedia, Factorial number system

Index entries for sequences related to factorial numbers

EXAMPLE

Triangle begins:

0

1

1,0

1,1

2,0

2,1

1,0,0

For example, 11 in base factorial is 121 (1*6 + 2*2 + 1*1), so row 11 is 1,2,1.

MAPLE

b:= proc(n, i) local r; `if`(n<i, [n],

      [b(iquo(n, i, 'r'), i+1)[], r])

    end:

T:= n-> b(n, 2)[]:

seq(T(n), n=0..50);  # Alois P. Heinz, Mar 19 2014

PROG

(Haskell)

a108731 n k = a108731_row n !! k

a108731_row 0 = [0]

a108731_row n = t n $ reverse $ takeWhile (<= n) $ tail a000142_list

   where t 0 []     = []

         t x (b:bs) = x' : t m bs where (x', m) = divMod x b

a108731_tabf = map a108731_row [0..]

-- Reinhard Zumkeller, Jun 04 2012

CROSSREFS

Cf: A084558, A007623.

Cf. A000142.

Sequence in context: A080844 A076626 A182886 * A235168 A060950 A039976

Adjacent sequences:  A108728 A108729 A108730 * A108732 A108733 A108734

KEYWORD

easy,nonn,tabf,base

AUTHOR

Franklin T. Adams-Watters, Jun 22 2005

EXTENSIONS

Added a(0)=0 and offset changed accordingly by Reinhard Zumkeller, Jun 04 2012

STATUS

approved

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Last modified October 25 14:15 EDT 2014. Contains 248544 sequences.