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Search: id:A076796
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| A076796 |
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Greedy powers of (pi/4): sum_{n=1..inf} (pi/4)^a(n) = 1. |
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5
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| 1, 7, 15, 24, 32, 39, 47, 59, 79, 88, 102, 111, 134, 148, 158, 164, 172, 190, 206, 214, 220, 233, 24, 1, 251, 263, 271, 283, 292, 307, 314, 322, 329, 337, 350, 358, 364, 373, 384, 399, 413, 438, 446, 456, 462, 475, 481, 494, 502, 51, 6, 529, 536, 552, 559, 567
(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/4) and frac(y) = y - floor(y).
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EXAMPLE
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a(3)=15 since (pi/4) +(pi/4)^7 +(pi/4)^15 < 1 and (pi/4) +(pi/4)^7 +(pi/4)^14 > 1; since the power 14 makes the sum > 1, then 15 is the 3rd greedy power of (pi/4).
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MAPLE
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Digits := 400: summe := 0.0: p := evalf(Pi / 4.): 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: A029724 A056828 A113505 this_sequence A056119 A082111 A012480
Adjacent sequences: A076793 A076794 A076795 this_sequence A076797 A076798 A076799
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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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