

A256100


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


6



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, 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, 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
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OFFSET

1,10


COMMENTS

The motivation to consider this sequence came from the proposal A256379 by Anthony Sand.
This sequence can also be read as an irregular triangle (array) in which a(n, k) is the number of appearances of the kth digit of n in the digits of 1, ... ,n1 and the first k digits of n. See the example for the head of this array. The row length is A055842(n), n >= 1.


LINKS



FORMULA

a(n) gives the number of digits A007376(n) in the sequence starting with A007376(1) and ending with A007376(n).


EXAMPLE

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.
Read as a tabf array a(n, k) with row length A055842(n) this begins:
n\k 1 2 ...
1: 1
2: 1
3: 1
4: 1
5: 1
6: 1
7: 1
8: 1
9: 1
10: 2 1
11: 3 4
12: 5 2
13: 6 2
14: 7 2
15: 8 2
16: 9 2
17: 10 2
18: 11 2
19: 12 2
20: 3 2
...


MATHEMATICA

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 *)


PROG

(Haskell)
a256100 n = a256100_list !! (n1)
a256100_list = f a007376_list $ take 10 $ repeat 1 where
f (d:ds) counts = y : f ds (xs ++ (y + 1) : ys) where
(xs, y:ys) = splitAt d counts


CROSSREFS



KEYWORD



AUTHOR



STATUS

approved



