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A265892 Array read by ascending antidiagonals: A(n,k) = A265893(A265609(n,k)), with n as row >= 0, k as column >= 0; the number of significant digits counted without trailing zeros in the factorial base representation of rising factorial n^(k) = (n+k-1)!/(n-1)!.

%I A265892 #17 Jun 03 2018 02:02:41
%S A265892 1,1,0,1,1,0,1,1,1,0,1,2,1,1,0,1,1,1,1,1,0,1,2,2,2,1,1,0,1,1,2,1,1,1,
%T A265892 1,0,1,3,2,3,2,2,1,1,0,1,2,3,2,2,3,1,1,1,0,1,3,1,2,3,1,2,2,1,1,0,1,2,
%U A265892 2,1,1,1,2,2,1,1,1,0,1,3,3,4,2,2,2,3,3,2,1,1,0,1,1,3,2,3,3,3,2,2,1,1,1,1,0,1,3,3,4,3,4,4,4,3,3,2,2,1,1,0
%N A265892 Array read by ascending antidiagonals: A(n,k) = A265893(A265609(n,k)), with n as row >= 0, k as column >= 0; the number of significant digits counted without trailing zeros in the factorial base representation of rising factorial n^(k) = (n+k-1)!/(n-1)!.
%C A265892 Square array A(row,col) is read by ascending antidiagonals as: A(0,0), A(1,0), A(0,1), A(2,0), A(1,1), A(0,2), A(3,0), A(2,1), A(1,2), A(0,3), ...
%H A265892 Antti Karttunen, <a href="/A265892/b265892.txt">Table of n, a(n) for n = 0..7259; the first 120 antidiagonals of array</a>
%H A265892 <a href="/index/Fa#facbase">Index entries for sequences related to factorial base representation</a>
%F A265892 A(n,k) = A265893(A265609(n,k)).
%e A265892 The top left corner of the array A265609 with its terms shown in factorial base (A007623) looks like this:
%e A265892 1,   0,    0,     0,       0,        0,         0,          0,           0
%e A265892 1,   1,   10,   100,    1000,    10000,    100000,    1000000,    10000000
%e A265892 1,  10,  100,  1000,   10000,   100000,   1000000,   10000000,   100000000
%e A265892 1,  11,  200,  2200,   30000,   330000,   4000000,   44000000,   500000000
%e A265892 1,  20,  310, 10000,  110000,  1220000,  14000000,  160000000,  1830000000
%e A265892 1,  21, 1100, 13300,  220000,  3000000,  36000000,  452000000,  5500000000
%e A265892 1, 100, 1300, 24000,  411000,  6000000,  82000000, 1100000000, 13300000000
%e A265892 1, 101, 2110, 41000, 1000000, 13000000, 174000000, 2374000000, 30360000000
%e A265892 -
%e A265892 Counting such digits for each term, but without the trailing zeros gives us the top left corner of this array:
%e A265892 -
%e A265892 The top left corner of the array:
%e A265892 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
%e A265892 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1
%e A265892 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1
%e A265892 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1
%e A265892 1, 1, 2, 1, 2, 3, 2, 2, 3, 1, 2, 3, 2, 2, 3, 1, 2, 3, 2, 2, 3, 1, 2, 3, 2
%e A265892 1, 2, 2, 3, 2, 1, 2, 3, 2, 3, 2, 3, 1, 2, 2, 3, 2, 3, 2, 3, 1, 2, 3, 4, 3
%e A265892 1, 1, 2, 2, 3, 1, 2, 2, 3, 4, 3, 1, 2, 3, 4, 2, 3, 2, 3, 4, 1, 2, 3, 3, 4
%e A265892 1, 3, 3, 2, 1, 2, 3, 4, 4, 4, 3, 4, 2, 3, 3, 4, 3, 4, 3, 3, 4, 2, 4, 5, 4
%e A265892 1, 2, 1, 1, 2, 3, 4, 3, 3, 2, 3, 2, 4, 5, 4, 3, 4, 3, 3, 4, 5, 3, 4, 3, 4
%e A265892 1, 3, 2, 4, 3, 4, 3, 4, 2, 3, 4, 5, 4, 3, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 3
%e A265892 1, 2, 3, 2, 3, 4, 3, 4, 5, 3, 4, 5, 3, 4, 5, 3, 4, 5, 5, 4, 5, 4, 5, 3, 4
%e A265892 1, 3, 3, 4, 4, 4, 3, 4, 4, 5, 4, 3, 3, 5, 6, 6, 5, 6, 5, 6, 5, 6, 4, 5, 6
%e A265892 1, 1, 3, 3, 3, 2, 3, 3, 4, 4, 5, 3, 4, 5, 5, 4, 5, 4, 5, 4, 5, 6, 4, 5, 4
%e A265892 1, 3, 4, 4, 4, 5, 4, 5, 5, 5, 5, 6, 4, 5, 6, 6, 5, 6, 5, 7, 6, 5, 5, 5, 5
%e A265892 1, 2, 3, 2, 4, 3, 4, 4, 4, 4, 5, 5, 6, 5, 5, 4, 6, 5, 6, 5, 4, 4, 4, 5, 6
%e A265892 1, 3, 1, 2, 3, 4, 5, 4, 3, 4, 4, 5, 5, 7, 6, 7, 6, 7, 5, 6, 7, 5, 4, 5, 6
%e A265892 1, 2, 4, 3, 5, 4, 3, 5, 6, 6, 5, 6, 6, 5, 6, 5, 6, 4, 5, 6, 4, 4, 6, 7, 8
%e A265892 1, 3, 3, 5, 4, 5, 5, 6, 5, 6, 5, 7, 6, 7, 6, 7, 4, 5, 6, 8, 5, 6, 7, 8, 6
%e A265892 1, 1, 3, 3, 4, 3, 5, 4, 5, 4, 6, 5, 6, 5, 6, 6, 7, 6, 7, 4, 5, 6, 7, 5, 6
%e A265892 ...
%o A265892 (Scheme)
%o A265892 (define (A265892 n) (A265892bi (A025581 n) (A002262 n)))
%o A265892 (define (A265892bi row col) (A265893 (A265609bi row col)))
%Y A265892 Cf. A007623, A265609.
%Y A265892 Row 0: A000007, rows 1-2: A000012, row 3: A000034 (see comment in A001710).
%Y A265892 Column 0: A000012, column 1: A265893.
%Y A265892 Cf. also array A265890.
%K A265892 nonn,tabl,base
%O A265892 0,12
%A A265892 _Antti Karttunen_, Dec 20 2015