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A020860
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Decimal expansion of log(7)/log(2).
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0
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2, 8, 0, 7, 3, 5, 4, 9, 2, 2, 0, 5, 7, 6, 0, 4, 1, 0, 7, 4, 4, 1, 9, 6, 9, 3, 1, 7, 2, 3, 1, 8, 3, 0, 8, 0, 8, 6, 4, 1, 0, 2, 6, 6, 2, 5, 9, 6, 6, 1, 4, 0, 7, 8, 3, 6, 7, 7, 2, 9, 1, 7, 2, 4, 0, 7, 0, 3, 2, 0, 8, 4, 8, 8, 6, 2, 1, 9, 2, 9, 8, 6, 4, 9, 7, 8, 6, 0, 9, 9, 9, 1, 7, 0, 2, 1, 0, 7, 8
(list; constant; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Log(base 2)7. Exponent in how, by recursive application of Strassen's algorithm, as shown in Nayebi, the product of two matrices can be computed by at most (4.7)*n^(log2(7)). Proof that this constant is irrational; by kb: Assume that log_2(7) = m/n for some positive integers m and n.
==>7 = 2^(m/n)
==> 7^n = 2^m.
This is a contradiction, because the left side is odd, while the right side is even [Jonathan Vos Post, Feb 16, 2011].
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REFERENCES
| V. Strassen, Gaussian elimination is not optimal, Numer. Math. 13 (1969): 354-356. MR 40:2223.
V. Pan, How can we speed up matrix multiplcation?, SIAM Review, 26 (1984): 393-416.
L. Adleman, Molecular Computation of Solutions to Combinatorial Problems, Science 266 (1994): 1021-1024.
S. Robinson, Toward an Optimal Algorithm for Matrix Multiplication, SIAM News 38 (2005): 1-3.
D. K. Nguyen, I. Lavall'ee, and M. Bui, A New Direction to Parallelize Winograd’s Algorithm on Distributed Memory Computers, Modeling, Simulation and Optimization of Complex Processes Proceedings of the Third International Conference
on High Performance Scientific Computing, March 6-10, 2006, Hanoi, Vietnam: 445-457.
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LINKS
| Aran Nayebi, Fast matrix multiplication techniques based on the Adleman-Lipton model, Feb 16, 2011.
Prove log(base 2)7 is rational?
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EXAMPLE
| 2.807354922.
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CROSSREFS
| Sequence in context: A188924 A011055 A195009 * A188934 A058655 A058964
Adjacent sequences: A020857 A020858 A020859 * A020861 A020862 A020863
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KEYWORD
| nonn,cons
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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