|
| |
|
|
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
|
| |
|
|
