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Search: id:A076797
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| A076797 |
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Greedy powers of (pi/5): sum_{n=1..inf} (pi/5)^a(n) = 1. |
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1
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| 1, 3, 5, 8, 15, 17, 20, 25, 28, 30, 32, 35, 43, 54, 58, 65, 67, 70, 73, 76, 82, 86, 89, 94, 97, 100, 107, 112, 119, 121, 124, 130, 133, 135, 137, 141, 143, 146, 153, 156, 163, 166, 169, 175, 177, 180, 185, 195, 199, 204, 210, 212, 217, 220, 226, 229, 234, 239
(list; graph; listen)
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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=(pi/5) and frac(y) = y - floor(y).
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EXAMPLE
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a(3)=? since (pi/5) +(pi/5)^3 +(pi/5)^5 < 1 and (pi/5) +(pi/5)^3 +(pi/5)^4 > 1; since the power 4 makes the sum > 1, then 5 is the 3rd greedy power of (pi/5).
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MAPLE
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Digits := 400: summe := 0.0: p := evalf(Pi / 5.): pexp := p: a := []: for i from 1 to 800 do: if summe + pexp < 1 then a := [op(a), i]: summe := summe + pexp: fi: pexp := pexp * p: od: a;
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CROSSREFS
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Cf. A077468 - A077475.
Sequence in context: A095290 A080999 A077579 this_sequence A052977 A099846 A141775
Adjacent sequences: A076794 A076795 A076796 this_sequence A076798 A076799 A076800
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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)
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EXTENSIONS
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Corrected by T. D. Noe (noe(AT)sspectra.com), Nov 02 2006
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