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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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82
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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;
text;
internal format)
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OFFSET
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1,2
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COMMENTS
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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Popular Computing (Calabasas, CA), Sieves: Problem 43, Vol. 2 (No. 13, Apr 1974), pp. 6-7. This is Sieve #1. [Annotated and scanned copy]
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FORMULA
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(End)
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MAPLE
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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:
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MATHEMATICA
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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 *)
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PROG
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(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])
(Scheme)
(define (A003309 n) (if (= 1 n) n (A255127bi (- n 1) 1))) ;; Code for A255127bi given in A255127.
(Python)
remainders = [0]
ludics = [2]
N_MAX = 313
for i in range(3, N_MAX) :
ludic_index = 0
while ludic_index < len(ludics) :
ludic = ludics[ludic_index]
remainder = remainders[ludic_index]
remainders[ludic_index] = (remainder + 1) % ludic
if remainders[ludic_index] == 0 :
break
ludic_index += 1
if ludic_index == len(ludics) :
remainders.append(0)
ludics.append(i)
ludics = [1] + ludics
print(ludics)
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CROSSREFS
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Without the initial 1 occurs as the leftmost column in arrays A255127 and A260717.
Cf. A192490 (characteristic function).
Cf. A237056, A237126, A237427, A235491, A255407, A255408, A255421, A255422, A260435, A260436, A260741, A260742 (permutations constructed from Ludic numbers).
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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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