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A003309
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Ludic numbers: apply the same sieve as Eratosthenes, but cross off every k-th /remaining/ number.
(Formerly M0655)
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13
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1, 2, 3, 5, 7, 11, 13, 17, 23, 25, 29, 37, 41, 43, 47, 53, 61, 67, 71, 77, 83, 89, 91, 97, 107, 115, 119, 121, 127, 131, 143, 149, 157, 161, 173, 175, 179, 181, 193, 209, 211, 221, 223, 227, 233, 235, 239, 247, 257, 265, 277, 283, 287, 301, 307, 313
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Complement of A192607; A192490(a(n) = 1. [Reinhard Zumkeller, Jul 05 2011]
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REFERENCES
| "Sieves", Popular Computing (Calabasas, CA), Vol. 2 (No. 13, Apr 1974), pp. 6-7; sieve #1.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| Donovan Johnson, Table of n, a(n) for n = 1..100000
D. Applegate, C program for A003309
Index entries for sequences generated by sieves
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MATHEMATICA
| t = Range[2, 400]; r = {1}; While[Length[t] > 0, k = First[t]; AppendTo[r, k]; t = Drop[t, {1, -1, k}]; ]; r (* from Ray Chandler, Dec 02 2004 *)
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PROG
| (PARI) t=vector(399, x, x+1); r=[1]; while(length(t)>0, k=t[1]; r=concat(r, [k]); t=vector((length(t)*(k-1))\k, x, t[(x*k+k-2)\(k-1)])); r - Phil Carmody (pc+oeis(AT)asdf.org), Feb 07 2007
(Haskell)
a003309 n = a003309_list !! (n-1)
a003309_list = 1 : sieve' [2..] where
sieve' (x:xs) = x : (sieve' $ sieving x xs) where
sieving k xs = (take (k-1) xs) ++ (sieving k $ drop k xs)
-- Reinhard Zumkeller, Jul 03 2011
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CROSSREFS
| Cf. A003310, A003311.
Cf. A192503 (primes), A192504 (non primes), A192512 (number of terms <= n).
Sequence in context: A175063 A198196 A139054 * A063884 A165671 A162855
Adjacent sequences: A003306 A003307 A003308 * A003310 A003311 A003312
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KEYWORD
| nonn,easy,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from D. Applegate and N. J. A. Sloane (njas(AT)research.att.com), Nov 23 2004
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