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Search: id:A076799
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| A076799 |
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Greedy powers of (e/3): sum_{n=1..inf} (e/3)^a(n) = 1. |
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1
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| 1, 24, 92, 140, 171, 199, 226, 251, 277, 320, 363, 391, 425, 449, 474, 500, 524, 548, 575, 632, 67, 3, 777, 801, 836, 861, 903, 932, 959, 983, 1011, 1054, 1087, 1113, 1148, 1176, 1228, 1261, 1286, 1316, 1348, 1394, 1427, 1452, 1480, 1510, 153, 6, 1571
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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=(e/3) and frac(y) = y - floor(y).
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EXAMPLE
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a(3)=92 since (e/3) +(e/3)^24 +(e/3)^92 < 1 and (e/3) +(e/3)^24 +(e/3)^91 > 1; since the power 91 makes the sum > 1, then 92 is the 4th greedy power of (e/3).
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MAPLE
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Digits := 1100: summe := 0.0: p := evalf(exp(1)/3.): pexp := p: a := []: for i from 1 to 3000 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: A044211 A044592 A010012 this_sequence A055671 A090214 A103251
Adjacent sequences: A076796 A076797 A076798 this_sequence A076800 A076801 A076802
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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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