|
%I
%S 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,
%T 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,
%U 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
%N Triangle read by rows: row n gives digits of n in base factorial.
%C Row lengths are A084558. This sequence contains every finite sequence of nonnegative integers.
%H _Reinhard Zumkeller_, <a href="/A108731/b108731.txt">Rows n = 0..2000 of triangle, flattened</a>
%H C. A. Laisant, <a href="http://www.numdam.org/item?id=BSMF_1888__16__176_0">Sur la numération factorielle, application aux permutations</a>, Bulletin de la Société Mathématique de France, 16 (1888), p. 176-183.
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Factoradic">Factorial number system</a>
%H <a href="/index/Fa#factorial">Index entries for sequences related to factorial numbers</a>
%e Triangle begins:
%e 1
%e 1,0
%e 1,1
%e 2,0
%e 2,1
%e 1,0,0
%e For example, 11 in base factorial is 121 (1*6 + 2*2 + 1*1), so row 11 is 1,2,1.
%o (Haskell)
%o a108731 n k = a108731_row n !! k
%o a108731_row 0 = [0]
%o a108731_row n = t n $ reverse $ takeWhile (<= n) $ tail a000142_list
%o where t 0 [] = []
%o t x (b:bs) = x' : t m bs where (x',m) = divMod x b
%o a108731_tabf = map a108731_row [0..]
%o -- _Reinhard Zumkeller_, Jun 04 2012
%Y Cf: A084558, A007623.
%Y Cf. A000142.
%K easy,nonn,tabf,base
%O 0,7
%A _Franklin T. Adams-Watters_, Jun 22 2005
%E Added a(0)=0 and offset changed accordingly by _Reinhard Zumkeller_, Jun 04 2012
|
