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

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, 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, 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

Offset

0,112

Comments

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.

Links

Robert Israel, Table of n, a(n) for n = 0..10009 (rows 0 to 1000, flattened)

Formula

From Robert Israel, Jul 08 2016: (Start)

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

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)

Maple

seq(seq(numboccur(k, convert(n, base, 10)), k=0..9), n=0..100); # Robert Israel, Jul 08 2016

Prog

(PARI) T(n, k) = #select(x->x==k, digits(n))+!(n+k); \\ Jinyuan Wang, Mar 01 2020

Crossrefs

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

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

Cf. A059995, A010879.

Sequence in context: A014856 A015703 A015582 * A369004 A359605 A368994

Adjacent sequences: A100907 A100908 A100909 * A100911 A100912 A100913

Keyword

nonn,base,easy,tabf

Author

Rick L. Shepherd, Nov 21 2004

Status

approved