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A047836
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"Nullwertzahlen" (or "inverse prime numbers"): n=p1*p2*p3*p4*p5*...*pk, where pi are primes with p1 <= p2 <= p3 <= p4 ...; then p1 = 2 and p1*p2*...*pi >= p(i+1) for all i < k.
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8
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2, 4, 8, 12, 16, 24, 32, 36, 40, 48, 56, 60, 64, 72, 80, 84, 96, 108, 112, 120, 128, 132, 144, 160, 168, 176, 180, 192, 200, 208, 216, 224, 240, 252, 256, 264, 280, 288, 300, 312, 320, 324, 336, 352, 360, 384, 392, 396, 400, 408, 416, 420, 432, 440, 448
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Start with n and reach 2 by repeatedly either dividing by d where d <= the square root or by adding or subtracting 1. The division steps are free, but adding or subtracting 1 costs 1 point. The "value" of n (A047988) is the smallest cost to reach 2. Sequence gives numbers with value 0.
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REFERENCES
| Thomas Kantke, Mathematische Unterhaltungen, Spectrum der Wissenschaft, No. 4, 1993, pp. 11-13.
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..1000
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FORMULA
| The number of a(n) <= x is conjectured to be about C * x / ln (x), where C = 0.61...
a(n) = 2 * A174973(n). [Reinhard Zumkeller, Sep 28 2011]
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EXAMPLE
| Starting at 24 we divide by 3, 2, then 2, reaching 2.
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PROG
| (Haskell)
a047836 n = a047836_list !! (n-1)
a047836_list = f [2] where
f (x:xs) = x : f (xs `merge` map (x *) [2..x])
-- Reinhard Zumkeller, Sep 28 2011
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CROSSREFS
| Cf. A047984-A047988.
Cf. A052287.
Sequence in context: A160736 A118030 A187208 * A181824 A070173 A116882
Adjacent sequences: A047833 A047834 A047835 * A047837 A047838 A047839
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KEYWORD
| nonn,nice,easy
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AUTHOR
| Thomas Kantke (bytes.more(AT)ibm.net)
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EXTENSIONS
| More terms from David W. Wilson (davidwwilson(AT)comcast.net)
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