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Search: id:A130320
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| A130320 |
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Given n numbers, n>(n-1)>(n-2)>...>2>1, adding the first and last numbers leads to equality, n+1 = (n-1)+2 = (n-2)+3 = ... and so on. In case if some positive x_1, x_2, ... are added to n, (n-1) etc, the strict inequality could be retained. This could be repeated finitely many times till it ends in inequality of form M > N where M-N is minimal. This sequence gives the value of M for different n. |
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+0
1
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| 1, 2, 4, 6, 10, 16, 18, 22, 34, 40, 56, 64, 66, 74, 78, 86, 130, 142, 148, 160, 216, 232, 240, 256, 258, 274, 282, 298, 302, 318
(list; graph; listen)
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OFFSET
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1,2
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LINKS
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Ramasamy Chandramouli, Table of n, a(n) for n = 1..17000
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FORMULA
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For n of form 2^k, we have a(n) = 4a(n-1) - 2 with a(1) = 2. For n of form 2^k + 2^(k-1), a(n) = 4a(n-1) with a(1) = 4.
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EXAMPLE
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a(5) = 10 because we have 5 > 4 > 3 > 2 > 1,
To follow a strict inequality, we would have, 5 + x > 4 + y > 3 > 2 > 1, where x > =0, y >= 0.
The next level of inequality gives, 1 + 5 + x > 2 + 4 + y > 3. This implies, x > y.
Continuing with next level gives 3 + 6 + x > 6 + y. This gives x = 1, y = 0.
Hence 10 > 6 giving a(5) = 10.
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CROSSREFS
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Adjacent sequences: A130317 A130318 A130319 this_sequence A130321 A130322 A130323
Sequence in context: A134682 A073805 A083814 this_sequence A101176 A131882 A073150
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KEYWORD
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nonn,uned
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AUTHOR
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Ramasamy Chandramouli (c.ramasamy(AT)gdatech.co.in), May 23 2007
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