

A003309


Ludic numbers: apply the same sieve as Eratosthenes, but cross off every kth /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
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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. 67; 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
David 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 (* 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)*(k1))\k, x, t[(x*k+k2)\(k1)])); 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: A248199 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



