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

1,2

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,..)

Links

Table of n, a(n) for n=1..86.

David Book, The Multiplying Digits Problem.

Example

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.

Crossrefs

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

Sequence in context: A233940 A134033 A185051 * A184997 A094367 A092368

Adjacent sequences: A095023 A095024 A095025 * A095027 A095028 A095029

Keyword

nonn,tabl,base

Author

Hugo Pfoertner, Jun 02 2004

Extensions

More terms from David Wasserman, Jun 03 2004

Status

approved