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A256100 In S = A007376 (read as a sequence) the digit S(n) appears a(n) times in the sequence S(1), ..., S(n).

%I A256100 #27 Mar 24 2017 00:47:57
%S A256100 1,1,1,1,1,1,1,1,1,2,1,3,4,5,2,6,2,7,2,8,2,9,2,10,2,11,2,12,2,3,2,4,
%T A256100 13,5,6,7,3,8,3,9,3,10,3,11,3,12,3,13,3,4,3,5,14,6,14,7,8,9,4,10,4,11,
%U A256100 4,12,4,13,4,14,4,5,4,6,15,7,15,8,15,9,10,11,5,12,5,13,5,14,5,15,5,6
%N A256100 In S = A007376 (read as a sequence) the digit S(n) appears a(n) times in the sequence S(1), ..., S(n).
%C A256100 The motivation to consider this sequence came from the proposal A256379 by Anthony Sand.
%C A256100 This sequence can also be read as an irregular triangle (array) in which a(n, k) is the number of appearances of the k-th digit of n in the digits of 1, ... ,n-1 and the first k digits of n. See the example for the head of this array. The row length is A055842(n), n >= 1.
%C A256100 This can also be described as the ordinal transform of A007376. - _Franklin T. Adams-Watters_, Oct 10 2015
%H A256100 Reinhard Zumkeller, <a href="/A256100/b256100.txt">Table of n, a(n) for n = 1..10000</a>
%F A256100 a(n) gives the number of digits A007376(n) in the sequence starting with A007376(1) and ending with A007376(n).
%e A256100 a(10) = 2 because A007376(10) = 1 and that sequence up to n=10 is 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, and 1 appears twice.
%e A256100 a(24) = 10 because A007376(24) = 1 and this is the tenth 1 in A007376 up to, and including, A007376(24).
%e A256100 Read as a tabf array a(n, k) with row length A055842(n) this begins:
%e A256100    n\k  1  2  ...
%e A256100    1:   1
%e A256100    2:   1
%e A256100    3:   1
%e A256100    4:   1
%e A256100    5:   1
%e A256100    6:   1
%e A256100    7:   1
%e A256100    8:   1
%e A256100    9:   1
%e A256100   10:   2  1
%e A256100   11:   3  4
%e A256100   12:   5  2
%e A256100   13:   6  2
%e A256100   14:   7  2
%e A256100   15:   8  2
%e A256100   16:   9  2
%e A256100   17:  10  2
%e A256100   18:  11  2
%e A256100   19:  12  2
%e A256100   20:   3  2
%e A256100   ...
%t A256100 lim = 120; s = Flatten[IntegerDigits /@ Range@ lim]; f[n_] := Block[{d = IntegerDigits /@ Take[s, n] // Flatten // FromDigits}, DigitCount[d][[If[ s[[n]] == 0, 10, s[[n]] ]] ] ]; Array[f, lim] (* _Michael De Vlieger_, Apr 08 2015, after _Robert G. Wilson v_ at A007376 *)
%o A256100 (Haskell)
%o A256100 a256100 n = a256100_list !! (n-1)
%o A256100 a256100_list = f a007376_list $ take 10 $ repeat 1 where
%o A256100    f (d:ds) counts = y : f ds (xs ++ (y + 1) : ys) where
%o A256100                            (xs, y:ys) = splitAt d counts
%o A256100 -- _Reinhard Zumkeller_, Aug 13 2015
%Y A256100 Cf. A007376, A065648.
%K A256100 nonn,base,easy,look
%O A256100 1,10
%A A256100 _Wolfdieter Lang_, Apr 08 2015