A007952 Generated by a sieve: keep first number, drop every 2nd, keep first, drop every 3rd, keep first, drop every 4th, etc.

0, 1, 3, 5, 9, 11, 17, 21, 29, 33, 41, 47, 57, 59, 77, 81, 101, 107, 117, 131, 149, 153, 173, 191, 209, 213, 239, 257, 273, 281, 321, 329, 359, 371, 401, 417, 441, 453, 497, 509, 539, 569, 611, 621, 647, 671, 717, 731, 779, 801, 839, 869, 917, 929, 989, 1001, 1053, 1067

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

A082447(n+1) = (number of terms <= n); see A141262 for primes. - Reinhard Zumkeller, Jun 21 2008

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!

Index entries for sequences generated by sieves

Formula

Equals A002491(n) - 1. Equals A108696 - 2.

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

Cf. A002491, A028920, A028931, A028932, A028933, A108696, A140060, A141271, A141272.

Sequence in context: A015614 A138203 A225523 * A145819 A317827 A296768

Adjacent sequences: A007949 A007950 A007951 * A007953 A007954 A007955

Keyword

nonn,easy,nice

Author

N. J. A. Sloane, R. Muller

Extensions

Corrected and extended by David W. Wilson

Status

approved