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A003309 Ludic numbers: apply the same sieve as Eratosthenes, but cross off every k-th /remaining/ number.
(Formerly M0655)
18
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; text; internal format)
OFFSET

1,2

COMMENTS

Complement of A192607; A192490(a(n) = 1. [Reinhard Zumkeller, Jul 05 2011]

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).

LINKS

Donovan Johnson, Table of n, a(n) for n = 1..100000

D. Applegate, C program for A003309

OEIS Wiki, Ludic numbers

Index entries for sequences generated by sieves

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 *)

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, Feb 07 2007

(Haskell)

a003309 n = a003309_list !! (n - 1)

a003309_list = 1 : f [2..] :: [Int]

   where f (x:xs) = x : f (map snd [(u, v) | (u, v) <- zip [1..] xs,

                                             mod u x > 0])

-- Reinhard Zumkeller, Feb 10 2014, Jul 03 2011

CROSSREFS

Cf. A003310, A003311.

Cf. A192503 (primes), A192504 (non primes), A192512 (number of terms <= n).

Cf. A237056, A237126.

Sequence in context: A175063 A198196 A139054 * A063884 A165671 A162855

Adjacent sequences:  A003306 A003307 A003308 * A003310 A003311 A003312

KEYWORD

nonn,easy,nice

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from David Applegate and N. J. A. Sloane, Nov 23 2004

STATUS

approved

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Last modified July 22 17:51 EDT 2014. Contains 244836 sequences.