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

Author

Rick L. Shepherd, Nov 21 2004

Keywords

• nonn
• base
• easy
• tabf

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)

Crossrefs

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

Cf. A055642 (row sums), A055641 (column 0), A268643 (column 1), A316863 (column 2), A316864 (column 3), A316865 (column 4), A316866 (column 5), A316867 (column 6), A316868 (column 7), A316869 (column 8), A102683 (column 9).

Cf. A059995, A010879.

Programs

Maple

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

Mathematica

A100910row[n_] := RotateRight[DigitCount[n]];
Array[A100910row, 10, 0] (* Paolo Xausa, Jul 16 2025 *)

PARI

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

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)