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Search: id:A079933
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| A079933 |
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Greedy powers of (1/sqrt(3)): sum_{n=1..inf} (1/sqrt(3))^a(n) = 1. |
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+0
4
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| 1, 2, 5, 7, 11, 12, 19, 22, 27, 33, 37, 39, 42, 44, 53, 54, 60, 62, 68, 69, 75, 77, 78, 83, 86, 87, 91, 94, 97, 100, 101, 105, 106, 110, 113, 115, 116, 120, 121, 125, 129, 131, 132, 137, 141, 144, 148, 149, 152, 155, 157, 166, 171, 173, 178, 179, 184, 186, 189, 191
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OFFSET
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1,2
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COMMENT
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The n-th greedy power of x, when 0.5 < x < 1, is the smallest integer exponent a(n) that does not cause the power series sum_{k=1..n} x^a(k) to exceed unity.
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FORMULA
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a(n)=sum_{k=1..n}floor(g_k) where g_1=1, g_{n+1}=log_x(x^frac(g_n) - x) (n>0) at x=(1/sqrt(3)) and frac(y) = y - floor(y).
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EXAMPLE
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a(3)=5 since (1/sqrt(3)) + (1/sqrt(3))^2 + (1/sqrt(3))^5 < 1 and (1/sqrt(3)) +(1/sqrt(3))^2 + (1/sqrt(3))^4 > 1; since the power 4 makes the sum > 1, then 5 is the 3th greedy power of (1/sqrt(3)).
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CROSSREFS
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Cf. A076796-A076802, A077468 - A077475, A079930 - A079932.
Sequence in context: A025062 A175034 A030498 this_sequence A075610 A057922 A113543
Adjacent sequences: A079930 A079931 A079932 this_sequence A079934 A079935 A079936
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KEYWORD
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easy,nonn
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AUTHOR
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Ulrich Schimke (ulrschimke(AT)aol.com), Jan 16 2003
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