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

0,3

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

Links

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

Formula

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

Example

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

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A023115 A194436 A061336 * A374438 A285730 A353655

Adjacent sequences: A057942 A057943 A057944 * A057946 A057947 A057948

Keyword

nonn

Author

Henry Bottomley, Oct 05 2000

Status

approved