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A353384
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Irregular triangle T(n,k) with row n listing A003592(j) not divisible by 20 such that A352218(A003592(j)) = n.
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1
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1, 2, 4, 5, 10, 8, 16, 25, 50, 32, 64, 125, 250, 128, 256, 625, 1250, 512, 1024, 3125, 6250, 2048, 4096, 15625, 31250, 8192, 16384, 78125, 156250, 32768, 65536, 390625, 781250, 131072, 262144, 1953125, 3906250, 524288, 1048576, 9765625, 19531250, 2097152, 4194304, 48828125, 97656250
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OFFSET
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0,2
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COMMENTS
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All terms in A003592 are products T(n,k)*20^j, j >= 0.
When expressed in base 20, T(n,k) does not end in zero, yet 1/T(n,k) is a terminating fraction, regular to 20.
The first 5 terms are the proper divisors of 20.
For these reasons, the terms may be called vigesimal "proper regular" numbers.
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REFERENCES
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G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, Chapter IX: The Representation of Numbers by Decimals, Theorem 136. 8th ed., Oxford Univ. Press, 2008, 144-145.
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LINKS
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Eric Weisstein's World of Mathematics, Vigesimal
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FORMULA
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Row 0 contains the empty product, thus row length = 1.
Row n sorts {2^(2n-1), 5^n, 2^(2n), 2*5^n}, thus row length = 4.
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EXAMPLE
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Row 0 contains 1 since 1 is the empty product.
Row 1 contains 2, 4, 5, and 10 since these divide 20 and are not divisible by 20.
Row 2 contains 8, 16, 25, and 50 since these divide 20^2 but not 20. The other divisors of 20^2 either divide smaller powers of 20 or they are divisible by 20 and do not appear.
Row 3 contains 32, 64, 125, and 250 since these divide 20^3 but not 20^2. The other divisors of 20^3 either divide smaller powers of 20 or they are divisible by 20 therefore do not appear.
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MATHEMATICA
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{{1}}~Join~Array[Union@ Flatten@ {#, 2 #} &@ {2^(2 # - 1), 5^#} &, 11] // Flatten
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CROSSREFS
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KEYWORD
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nonn,easy,base,tabf
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AUTHOR
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STATUS
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approved
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