cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A082447 a(n) = the number k such that s(k)=0 where s(0)=n and s(i)=s(i-1)-(s(i-1) modulo (i+1)).

Original entry on oeis.org

1, 2, 2, 3, 3, 4, 4, 4, 4, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 13, 13, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 15, 15, 15
Offset: 1

Views

Author

Benoit Cloitre, Apr 25 2003

Keywords

Comments

a(n+1) = number of Mancala numbers <= n, see A007952; n occurs A028913(n-1) times consecutively. - Reinhard Zumkeller, Jun 21 2008
a(n) = number of ones <= n in A130747; see also A002491. - Reinhard Zumkeller, Jul 01 2009

Examples

			For n=4, s(0)=4, 4 ->4-4 mod 1=4 ->4-4 mod 2=4 ->4-4 mod 3=3 ->3-3 mod 4=0, hence s(4)=0 and a(4)=4.
For n=6, s(0)=6, s(1)=6-6 mod 2=6, s(2)=6-6 mod 3=6, s(3)=6-6 mod 4=6-2=4, s(4)=4-4 mod 5=0, hence a(6)=4.

Links

Crossrefs

Cf. A073047, A140060, A140061.

Programs

  • Mathematica
    Flatten@Table[First@Position[Rest@FoldList[#1-Mod[#1,#2]&,i,Range[2,i+1]],0], {i,30}] (* Birkas Gyorgy, Feb 26 2011 *)
  • PARI
    a(n)=if(n<1, 0, s=n; c=1; while(s-s%c>0, s=s-s%c; c++); c--) \\ corrected by Dan Dima, Jan 18 2025

Formula

Conjecture: a(n) = sqrt(Pi*n) + O(1)
a(n) = A073047(n) - 1.

Extensions

Name corrected by Dan Dima, Jan 18 2025

A028913 First differences of A007952.

Original entry on oeis.org

1, 2, 2, 4, 2, 6, 4, 8, 4, 8, 6, 10, 2, 18, 4, 20, 6, 10, 14, 18, 4, 20, 18, 18, 4, 26, 18, 16, 8, 40, 8, 30, 12, 30, 16, 24, 12, 44, 12, 30, 30, 42, 10, 26, 24, 46, 14, 48, 22, 38, 30, 48, 12, 60, 12, 52, 14, 54, 52, 26, 12, 66, 54, 60, 10, 26, 60, 60, 10, 74, 30, 52, 56, 64, 14, 34
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A082447, A140060, A140061.

Extensions

More terms from Reinhard Zumkeller, Jun 21 2008

A140060 Array of quotients.

Original entry on oeis.org

1, 2, 2, 3, 2, 4, 4, 3, 5, 4, 3, 6, 6, 6, 4, 7, 6, 6, 4, 8, 8, 6, 4, 9, 8, 6, 4, 10, 10, 9, 8, 5, 11, 10, 9, 8, 5, 12, 12, 12, 12, 10, 6, 13, 12, 12, 12, 10, 6, 14, 14, 12, 12, 10, 6, 15, 14, 12, 12, 10, 6, 16, 16, 15, 12, 10, 6, 17, 16, 15, 12, 10, 6, 18, 18, 18, 16, 15, 12, 7, 19, 18, 18
Offset: 1

Views

Author

Clark Kimberling, May 03 2008

Keywords

Comments

1. k divides Q(n,k) for each k.
2. The numbers in row n are distinct if and only if n is a term of the Sieve of Tchoukaillon (or Mancala, or Kalahari), A007952.

Examples

			First 8 rows:
1
2 2
3 2
4 4 3
5 4 3
6 6 6 4
7 6 6 4
8 8 6 4
For row 5: Q(5,1)=5, Q(5,2)=2*[5/2]=4, Q(5,3)=3*[4/3]=3.

Crossrefs

Cf. A140061.

Formula

For n>=1, for k=1,2,...,A082447(n), Q(n,1)=n, Q(n,k)=k*Floor(Q(n,k-1)/k).
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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