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A095026
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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.
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0
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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
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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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,..)
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LINKS
| David Book, The Multiplying Digits Problem.
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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.
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CROSSREFS
| The first column T(n, 1)=A018804(n).
Sequence in context: A102573 A134033 A185051 * A184997 A094367 A092368
Adjacent sequences: A095023 A095024 A095025 * A095027 A095028 A095029
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KEYWORD
| nonn,tabl
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AUTHOR
| Hugo Pfoertner (hugo(AT)pfoertner.org), Jun 02 2004
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EXTENSIONS
| More terms from David Wasserman (dwasserm(AT)earthlink.net), Jun 03 2004
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