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Search: id:A079931
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| A079931 |
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Greedy powers of (1/sqrt(pi)): sum_{n=1..inf} (1/sqrt(pi))^a(n) = 1. |
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3
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| 1, 2, 4, 8, 9, 16, 20, 22, 23, 32, 33, 36, 39, 42, 43, 46, 47, 50, 51, 55, 59, 60, 63, 69, 74, 77, 80, 82, 87, 92, 94, 97, 100, 102, 105, 107, 111, 113, 114, 117, 119, 122, 126, 128, 129, 134, 141, 142, 146, 147, 150, 151, 154, 157, 160, 162, 165, 167, 168, 171, 175
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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(pi)) and frac(y) = y - floor(y).
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EXAMPLE
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a(3)=4 since (1/sqrt(pi)) + (1/sqrt(pi))^2 + (1/sqrt(pi))^4 < 1 and (1/sqrt(pi)) +(1/sqrt(pi))^2 + (1/sqrt(pi))^3 > 1; since the power 3 makes the sum > 1, then 4 is the 3th greedy power of (1/sqrt(pi)).
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CROSSREFS
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Cf. A076796-A076802, A077468 - A077475, A079930, A079932, A079933.
Sequence in context: A080025 A025611 A049439 this_sequence A055008 A046678 A046680
Adjacent sequences: A079928 A079929 A079930 this_sequence A079932 A079933 A079934
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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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