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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-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 * 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 April 13 09:12 EDT 2021. Contains 342935 sequences. (Running on oeis4.)