OFFSET
1,2
COMMENTS
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.
Donovan Johnson, Ludic numbers computed up to A003309(1236290) = 23000711.
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]
Rosettacode Wiki, Ludic numbers.
FORMULA
From Antti Karttunen, Feb 23 2015: (Start)
(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)
;; Antti Karttunen, Feb 23 2015
(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)
# Alexandre Herrera, Aug 10 2023
CROSSREFS
KEYWORD
nonn,easy,nice
AUTHOR
EXTENSIONS
More terms from David Applegate and N. J. A. Sloane, Nov 23 2004
STATUS
approved