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Search: id:A076802
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| A076802 |
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Greedy powers of the gamma constant (0.577215664...) sum_{n=1..inf} (gamma)^a(n) = 1. |
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+0
6
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| 1, 2, 5, 7, 10, 18, 20, 22, 23, 26, 30, 33, 37, 41, 44, 46, 48, 49, 53, 56, 58, 59, 68, 69, 75, 77, 78, 81, 88, 90, 94, 96, 98, 100, 102, 105, 106, 109, 111, 116, 120, 122, 124, 126, 132, 135, 137, 140, 145, 152, 155, 157, 158, 162, 165, 168, 171, 174, 176, 178
(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=gamma and frac(y) = y - floor(y).
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EXAMPLE
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a(3)=5 since (gamma) +(gamma)^2 +(gamma)^5 < 1 and (gamma) +(gamma)^2 +(gamma)^4 > 1; since the power 4 makes the sum > 1, then 5 is the 3th greedy power of gamma.
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MAPLE
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Digits := 400: summe := 0.0: p := evalf(gamma): 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: A102339 A103871 A068817 this_sequence A024374 A065219 A013660
Adjacent sequences: A076799 A076800 A076801 this_sequence A076803 A076804 A076805
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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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