OFFSET
0,3
COMMENTS
Also called the sieve of Tchoukaillon (or Mancala, or Kalahari).
If k+1 occurs at rank i for the first time, then i is given by the program: i = 0: for j = k to 1 step -1: i = 1 + i + int ( i / j ): next: - Claude Lenormand (claude.lenormand(AT)free.fr), Jan 15 2001
REFERENCES
Y. David, On a sequence generated by a sieving process, Riveon Lematematika, 11 (1957), 26-31.
M. Le, On the Smarandache n-ary Sieve, Smarandache Notions Journal, Vol. 10, No. 1-2-3, 1999, 146-147.
LINKS
L. K. Mitchell, Table of n, a(n) for n = 0..7549
D. Betten, Kalahari and the Sequence "Sloane No. 377", Annals Discrete Math., 37, 51-58, 1988.
D. M. Broline and Daniel E. Loeb, The combinatorics of Mancala-Type games: Ayo, Tchoukaillon and 1/Pi, arXiv:math/9502225 [math.CO], 1995; J. Undergrad. Math. Applic., vol. 16 (1995), pp. 21-36.
P. Erdős and E. Jabotinsky, On a sequence of integers ..., Indagationes Math., 20, 115-128, 1958. part I part II
N. J. A. Sloane, My favorite integer sequences, in Sequences and their Applications (Proceedings of SETA '98).
F. Smarandache, Only Problems, Not Solutions!
MATHEMATICA
f[n_] := Fold[#2*Floor[#1/#2 + 1] &, n, Reverse@ Range[n - 1]]; Array[f, 55] (* From David Wilson *)
PROG
(Haskell)
a007952 n = a007952_list !! n
a007952_list = f 1 [0..] where
f k (x:xs) = x : f (k + 1) (g xs) where
g ws = us ++ (g vs) where (us, _:vs) = splitAt k ws
-- Reinhard Zumkeller, Jan 19 2014
(PARI) a(n) = my(ret=0); forstep(k=n, 1, -1, ret++; ret+=(-ret)%k); ret; \\ Kevin Ryde, Sep 30 2022
CROSSREFS
KEYWORD
nonn,easy,nice
AUTHOR
N. J. A. Sloane, R. Muller
EXTENSIONS
Corrected and extended by David W. Wilson
STATUS
approved