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%I #27 Mar 24 2017 00:47:57
%S 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 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 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 In S = A007376 (read as a sequence) the digit S(n) appears a(n) times in the sequence S(1), ..., S(n).
%C The motivation to consider this sequence came from the proposal A256379 by Anthony Sand.
%C 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 This can also be described as the ordinal transform of A007376. - _Franklin T. Adams-Watters_, Oct 10 2015
%H Reinhard Zumkeller, <a href="/A256100/b256100.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) gives the number of digits A007376(n) in the sequence starting with A007376(1) and ending with A007376(n).
%e 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 a(24) = 10 because A007376(24) = 1 and this is the tenth 1 in A007376 up to, and including, A007376(24).
%e Read as a tabf array a(n, k) with row length A055842(n) this begins:
%e n\k 1 2 ...
%e 1: 1
%e 2: 1
%e 3: 1
%e 4: 1
%e 5: 1
%e 6: 1
%e 7: 1
%e 8: 1
%e 9: 1
%e 10: 2 1
%e 11: 3 4
%e 12: 5 2
%e 13: 6 2
%e 14: 7 2
%e 15: 8 2
%e 16: 9 2
%e 17: 10 2
%e 18: 11 2
%e 19: 12 2
%e 20: 3 2
%e ...
%t 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 (Haskell)
%o a256100 n = a256100_list !! (n-1)
%o a256100_list = f a007376_list $ take 10 $ repeat 1 where
%o f (d:ds) counts = y : f ds (xs ++ (y + 1) : ys) where
%o (xs, y:ys) = splitAt d counts
%o -- _Reinhard Zumkeller_, Aug 13 2015
%Y Cf. A007376, A065648.
%K nonn,base,easy,look
%O 1,10
%A _Wolfdieter Lang_, Apr 08 2015
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