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Search: id:A079932
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| A079932 |
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Greedy powers of (1/sqrt(2)): sum_{n=1..inf} (1/sqrt(2))^a(n) = 1. |
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+0
3
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| 1, 4, 10, 13, 22, 27, 32, 36, 40, 49, 54, 62, 66, 71, 80, 91, 97, 102, 109, 114, 120, 124, 127, 138, 146, 149, 159, 165, 169, 180, 184, 187, 194, 202, 208, 219, 224, 231, 235, 248, 258, 263, 266, 274, 281, 287, 294, 300, 304, 308, 316, 323, 329, 337, 343, 350
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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(2)) and frac(y) = y - floor(y).
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EXAMPLE
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a(3)=10 since (1/sqrt(2)) + (1/sqrt(2))^4 + (1/sqrt(2))^10 < 1 and (1/sqrt(2)) +(1/sqrt(2))^4 + (1/sqrt(2))^9 > 1; since the power 9 makes the sum > 1, then 10 is the 3th greedy power of (1/sqrt(2)).
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CROSSREFS
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Cf. A076796-A076802, A077468 - A077475, A079930, A079931, A079933.
Sequence in context: A143804 A152843 A139121 this_sequence A076270 A032821 A101576
Adjacent sequences: A079929 A079930 A079931 this_sequence A079933 A079934 A079935
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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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