A095026 Lower triangle T(j,k) read by rows, where T(j,k) is the number of occurrences of the digit k-1 as least significant digit in the base-j multiplication table.

1, 3, 1, 5, 2, 2, 8, 2, 4, 2, 9, 4, 4, 4, 4, 15, 2, 6, 5, 6, 2, 13, 6, 6, 6, 6, 6, 6, 20, 4, 8, 4, 12, 4, 8, 4, 21, 6, 6, 12, 6, 6, 12, 6, 6, 27, 4, 12, 4, 12, 9, 12, 4, 12, 4, 21, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 40, 4, 8, 10, 16, 4, 20, 4, 16, 10, 8, 4, 25, 12, 12, 12, 12, 12, 12, 12

Offset: 1

Author

Hugo Pfoertner, Jun 02 2004

Keywords

• nonn
• tabl
• base

Comments

Sum_{k=1..j} T(j,k) = j^2.

Assumes a suitable continuation of the representation of digits in bases 11, 12 (9,A,B,..)

Examples

			a(2)=T(2,1)=3 because 3 of the 4 possible combinations of last digits in the
product of two binary numbers produce 0 as last digit of the result. a(3)=T(2,2)=1 because only ...1 * ...1 gives a result with last digit=1.
T(10,k)={27,4,12,4,12,9,12,4,12,4} gives the probability in percent (j^2=100) to get {0,1,2,...,9} as last decimal digit in the decimal representation of the product of two arbitrary integers.
		

Links

• David Book, The Multiplying Digits Problem.

Crossrefs

The first column T(n, 1)=A018804(n).

Extensions

More terms from David Wasserman, Jun 03 2004