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

Author

N. J. A. Sloane, R. Muller

Keywords

• nonn
• easy
• nice

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

Crossrefs

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

Programs

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

Mathematica

f[n_] := Fold[#2*Floor[#1/#2 + 1] &, n, Reverse@ Range[n - 1]]; Array[f, 55] (* From David Wilson *)

PARI

a(n) = my(ret=0); forstep(k=n,1,-1, ret++; ret+=(-ret)%k); ret; \\ Kevin Ryde, Sep 30 2022

Formula

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

Extensions

Corrected and extended by David W. Wilson