A057945 Number of triangular numbers needed to represent n with greedy algorithm.

0, 1, 2, 1, 2, 3, 1, 2, 3, 2, 1, 2, 3, 2, 3, 1, 2, 3, 2, 3, 4, 1, 2, 3, 2, 3, 4, 2, 1, 2, 3, 2, 3, 4, 2, 3, 1, 2, 3, 2, 3, 4, 2, 3, 4, 1, 2, 3, 2, 3, 4, 2, 3, 4, 3, 1, 2, 3, 2, 3, 4, 2, 3, 4, 3, 2, 1, 2, 3, 2, 3, 4, 2, 3, 4, 3, 2, 3, 1, 2, 3, 2, 3, 4, 2, 3, 4, 3, 2, 3, 4, 1, 2, 3, 2, 3, 4, 2, 3, 4, 3, 2, 3, 4, 3

Offset: 0

Author

Henry Bottomley, Oct 05 2000

Keywords

• nonn

Comments

a(n) = sum of digits of A000462(n). - Reinhard Zumkeller, Mar 27 2011

The length of (number of moves in) Simon Norton's game in A006019 starting with an initial heap of n if both players always take, never put. - R. J. Mathar, May 13 2016

Examples

			a(35)=3 since 35=28+6+1
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A000217, A002262, A056944, A057944. See A006893 for records.

Programs

Haskell

a057945 n = g n $ reverse $ takeWhile (<= n) $ tail a000217_list where
   g 0 _      = 0
   g x (t:ts) = g r ts + a where (a,r) = divMod x t
-- Reinhard Zumkeller, Mar 27 2011

Maple

A057945 := proc(n)
    local a,x;
    a := 0 ;
    x := n ;
    while x > 0 do
        x := x-A057944(x) ;
        a := a+1 ;
    end do:
    a ;
end proc: # R. J. Mathar, May 13 2016

Mathematica

A057944[n_] := With[{k = Floor[Sqrt[8n+1]]}, Floor[(k-1)/2]* Floor[(k+1)/2]/2];
a[n_] := Module[{k = 0, x = n}, While[x>0, x = x - A057944[x]; k++]; k];
Table[a[n], {n, 0, 104}] (* Jean-François Alcover, Mar 10 2019, after R. J. Mathar *)

Formula

a(0)=0, otherwise a(n)=a(A002262(n))+1.