

A095026


Lower triangle T(j,k) read by rows, where T(j,k) is the number of occurrences of the digit k1 as least significant digit in the basej multiplication table.


1



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
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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



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).


KEYWORD



AUTHOR



EXTENSIONS



STATUS

approved



