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Search: id:A100617
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| A100617 |
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There are n people in a room. First half (i.e. [n/2]) of them leave, then 1/3 (i.e. floor of 1/3) of those remaining leave, then 1/4, then 1/5, etc.; sequence gives number who remain at the end. |
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+0
2
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| 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11
(list; graph; listen)
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OFFSET
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1,3
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REFERENCES
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V. Brun, Un proc\'{e}d\'{e} qui ressemble au crible d'Eratostene, Analele Stiintifice Univ. "Al. I. Cuza", Iasi, Romania, Sect. Ia Matematica, 1965, vol. 11B, pp. 47-53.
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FORMULA
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a(n) = k for Fl(k) <= n < Fl(k+1), where Fl(i) = A000960(i).
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EXAMPLE
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7 -> 7 - [7/2] = 7 - 3 = 4 -> 4 - [4/3] = 4 - 1 = 3 -> 3 - [3/4] = 3 - 0 = 3, which is now fixed, so a(7) = 3.
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MAPLE
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f:=proc(n) local i, j, k; k:=n; for i from 2 to 10000 do j := floor(k/i); if j < 1 then break; fi; k := k-j; od; k; end;
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CROSSREFS
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Cf. A000960, A100618.
Sequence in context: A003058 A000194 A097429 this_sequence A076471 A165116 A111656
Adjacent sequences: A100614 A100615 A100616 this_sequence A100618 A100619 A100620
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KEYWORD
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nonn,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Dec 03 2004
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