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A100910 Table of number of occurrences in n of each decimal digit from 0 to 9. 11

%I #28 Jan 08 2023 07:59:29

%S 1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,

%T 0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,

%U 0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,1,1,0,0,0

%N Table of number of occurrences in n of each decimal digit from 0 to 9.

%C Each row of this table has length 10 and corresponds to one term of A100909. n = 0 is normally represented as the single digit 0, so the first row here is 1, 0, 0, 0, 0, 0, 0, 0, 0, 0.

%H Robert Israel, <a href="/A100910/b100910.txt">Table of n, a(n) for n = 0..10009</a> (rows 0 to 1000, flattened)

%F From _Robert Israel_, Jul 08 2016: (Start)

%F a(n,k) = a(A059995(n),k) + (1 if A010879(n)=k, otherwise 0).

%F G.f. g(x,y) satisfies g(x,y) = ((1-x^10)/(1-x))*g(x^10,y) + (x^10-x)/(1-x) + x^10/(1-x^10) + x*y*(1-x^9*y^9)/((1-x^10)*(1-x*y)). (End)

%p seq(seq(numboccur(k, convert(n,base,10)),k=0..9),n=0..100); # _Robert Israel_, Jul 08 2016

%o (PARI) T(n, k) = #select(x->x==k, digits(n))+!(n+k); \\ _Jinyuan Wang_, Mar 01 2020

%Y Cf. A100909 (similar but each row of A100910 provides one A100909 term).

%Y Cf. A055642 (row sums), A055641 (column 0), A268643 (column 1), A102683 (column 9).

%Y Cf. A059995, A010879.

%K nonn,base,easy,tabf

%O 0,112

%A _Rick L. Shepherd_, Nov 21 2004

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Last modified April 25 08:25 EDT 2024. Contains 371964 sequences. (Running on oeis4.)