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

A082527 Least k such that x(k)=0 where x(1)=n x(k)=k^2*floor(x(k-1)/k^2).

Original entry on oeis.org

1, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8
Offset: 0

Views

Author

Benoit Cloitre, Apr 30 2003

Keywords

Examples

			If x(1)=3 x(2)=4*floor(3/4)=0 hence a(3)=2, if x(1)=10 x(2)=4*floor(10/4)=2 x(3)=0 hence a(10)=3...

Crossrefs

Cf. A073047.

Programs

  • PARI
    a(n)=if(n<0,0,s=n; c=1; while(s-s%(c^2)>0,s=s-s%(c^2); c++); c)

Formula

a(n) seems to be asymptotic to (c*n)^(1/3) where c=4.96....

A082528 Least k such that x(k)=0 where x(1)=n x(k)=k^3*floor(x(k-1)/k^3).

Original entry on oeis.org

1, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5
Offset: 0

Views

Author

Benoit Cloitre, Apr 30 2003

Keywords

Comments

Conjecture : define sequence a(n,m) m real >0 as the least k such that x(k)=0 where x(1)=n x(k)=k^m*floor(x(k-1)/k^m) then a(n,m) is asymptotic to (c(m)*n)^(1/(m+1)). where c(m) is a constant depending on m.

Crossrefs

Cf. A073047.

Programs

  • PARI
    a(n)=if(n<0,0,s=n; c=1; while(s-s%(c^3)>0,s=s-s%(c^3); c++); c)

Formula

a(n) seems to be asymptotic to (c*n)^(1/4) where c=6.76....
Showing 1-3 of 3 results.

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