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A007952
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Generated by a sieve: keep first number, drop every 2nd, keep first, drop every 3rd, keep first, drop every 4th, etc.
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23
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0, 1, 3, 5, 9, 11, 17, 21, 29, 33, 41, 47, 57, 59, 77, 81, 101, 107, 117, 131, 149, 153, 173, 191, 209, 213, 239, 257, 273, 281, 321, 329, 359, 371, 401, 417, 441, 453, 497, 509, 539, 569, 611, 621, 647, 671, 717, 731, 779, 801, 839, 869, 917, 929, 989, 1001, 1053, 1067
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,3
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COMMENTS
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Also called the sieve of Tchoukaillon (or Mancala, or Kalahari).
If k+1 occurs at rank i for the first time, then i is given by the program: i = 0: for j = k to 1 step -1: i = 1 + i + int ( i / j ): next: - Claude Lenormand (claude.lenormand(AT)free.fr), Jan 15 2001
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REFERENCES
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Y. David, On a sequence generated by a sieving process, Riveon Lematematika, 11 (1957), 26-31.
M. Le, On the Smarandache n-ary Sieve, Smarandache Notions Journal, Vol. 10, No. 1-2-3, 1999, 146-147.
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LINKS
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P. Erdős and E. Jabotinsky, On a sequence of integers ..., Indagationes Math., 20, 115-128, 1958. part I part II
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FORMULA
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MATHEMATICA
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f[n_] := Fold[#2*Floor[#1/#2 + 1] &, n, Reverse@ Range[n - 1]]; Array[f, 55] (* From David Wilson *)
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PROG
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(Haskell)
a007952 n = a007952_list !! n
a007952_list = f 1 [0..] where
f k (x:xs) = x : f (k + 1) (g xs) where
g ws = us ++ (g vs) where (us, _:vs) = splitAt k ws
(PARI) a(n) = my(ret=0); forstep(k=n, 1, -1, ret++; ret+=(-ret)%k); ret; \\ Kevin Ryde, Sep 30 2022
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CROSSREFS
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KEYWORD
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nonn,easy,nice
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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