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Search: id:A076798
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| A076798 |
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Greedy powers of (pi/6): sum_{n=1..inf} (pi/6)^a(n) = 1. |
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+0
1
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| 1, 2, 3, 5, 7, 8, 10, 11, 12, 14, 20, 21, 22, 25, 28, 33, 35, 37, 38, 39, 44, 45, 47, 49, 50, 52, 55, 56, 58, 59, 61, 63, 64, 71, 72, 78, 83, 84, 85, 88, 89, 93, 94, 96, 98, 100, 101, 104, 105, 106, 109, 114, 116, 117, 120, 121, 122, 125, 133, 134, 138, 140, 141, 142
(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/6) and frac(y) = y - floor(y).
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EXAMPLE
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a(4)=5 since (pi/6) +(pi/6)^2 +(pi/6)^3 +(pi/6)^5 < 1 and (pi/6) +(pi/6)^2 +(pi/6)^3 +(pi/6)^4 > 1; since the power 4 makes the sum > 1, then 5 is the 4th greedy power of (pi/6).
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MAPLE
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Digits := 400: summe := 0.0: p := evalf(Pi / 6.): 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: A028788 A034707 A156247 this_sequence A047488 A066093 A022342
Adjacent sequences: A076795 A076796 A076797 this_sequence A076799 A076800 A076801
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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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