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A057945 Number of triangular numbers needed to represent n with greedy algorithm. 8
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois 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 * A285730 A280055 A253092

Adjacent sequences:  A057942 A057943 A057944 * A057946 A057947 A057948

KEYWORD

nonn

AUTHOR

Henry Bottomley, Oct 05 2000

STATUS

approved

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Last modified August 25 13:50 EDT 2019. Contains 326324 sequences. (Running on oeis4.)