A006019 -id:A006019 - cp's OEIS frontend

A266726 Indices of even terms in A006019.

0, 2, 4, 9, 11, 13, 18, 20, 22, 24, 26, 29, 31, 37, 39, 41, 42, 44, 46, 48, 50, 51, 52, 56, 58, 60, 61, 62, 63, 65, 67, 72, 74, 79, 83, 84, 85, 86, 88, 90, 92, 94, 98, 99, 101, 103, 108, 110, 112, 119, 126, 128, 130, 135, 137, 139, 141, 142, 143, 144, 150, 151, 152, 154, 156, 158

Offset: 1

N. J. A. Sloane, Jan 03 2016

nonn

E. R. Berlekamp, J. H. Conway and R. K. Guy, Winning Ways, Academic Press, NY, 2 vols., 1982, see p. 502.
R. K. Guy, Fair Game: How to play impartial combinatorial games, COMAP's Mathematical Exploration Series, 1989; see p. 88.

Cf. A006019.

Extended beyond 72 by R. J. Mathar, May 07 2016

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

Original entry on oeis.org

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

Henry Bottomley, Oct 05 2000

nonn

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

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

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

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

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

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

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 *)

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

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A266726 Indices of even terms in A006019.

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

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