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A003309 Ludic numbers: apply the same sieve as Eratosthenes, but cross off every k-th /remaining/ number.
(Formerly M0655)
37
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

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

Popular Computing (Calabasas, CA), Sieves: Problem 43, Vol. 2 (No. 13, Apr 1974), pp. 6-7. This is Sieve #1. [Annotated and scanned copy]

Index entries for sequences generated by sieves

FORMULA

From Antti Karttunen, Feb 23 2015: (Start)

a(n) = A255407(A008578(n))

a(n) = A008578(n) + A255324(n).

(End)

MAPLE

ludic:= proc(N) local i, k, S, R;

  S:= {$2..N};

  R:= 1;

  while nops(S) > 0 do

    k:= S[1];

    R:= R, k;

    S:= subsop(seq(1+k*j=NULL, j=0..floor((nops(S)-1)/k)), S);

  od:

[R];

end proc:

ludic(1000); # Robert Israel, Feb 23 2015

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)*(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

(Scheme)

(define (A003309 n) (if (= 1 n) n (A255127bi (- n 1) 1))) ;; Code for A255127bi given in A255127.

;; Antti Karttunen, Feb 23 2015

CROSSREFS

Column 1 of array A255127 (row 1 of A255129), without the initial 1.

Cf. A003310, A003311, A100464, A100585, A100586 (variants).

Cf. A192503 (primes in sequence), A192504 (nonprimes), A192512 (number of terms <= n).

Cf. A192490 (characteristic function).

Cf. A192607 (complement).

Cf. A255420 (iterates of f(n) = A003309(n+1) starting from n=1).

Cf. A237056, A237126, A237427, A235491, A255407, A255408, A255421, A255422 (related permutations).

Cf. also A000959, A008578, A255324, A254100.

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

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Last modified July 31 07:09 EDT 2015. Contains 260159 sequences.