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A082447
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a(n) = the number k such that s(k)=0 where s(0)=n and s(i)=s(i-1)-(s(i-1) modulo i).
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6
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1, 2, 2, 3, 3, 4, 4, 4, 4, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 13, 13, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 15, 15, 15
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history;
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OFFSET
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1,2
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COMMENTS
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a(n+1) = number of Mancala numbers <= n, see A007952; n occurs A028913(n-1) times consecutively. - Reinhard Zumkeller, Jun 21 2008
a(n) = number of ones <= n in A130747; see also A002491. - Reinhard Zumkeller, Jul 01 2009
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LINKS
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R. Zumkeller, Table of n, a(n) for n = 1..10000
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FORMULA
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Conjecture: a(n) = sqrt(Pi*n) + O(1)
a(n) = A073047(n) - 1.
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EXAMPLE
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If n=6 : s(0)=6, s(1)=6-6 mod 2=6, s(2)=6-6 mod 3=6, s(3)=6-6 mod 4=6-2=4, s(4)=4-4 mod 5=0, hence a(6)=4.
If s(0)=4, 4 ->4-4 mod 1=4 ->4-4 mod 2=4 ->4-4 mod 3=3 ->3-3 mod 4=0, hence s(4)=0 and a(4)=4.
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MATHEMATICA
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Flatten@Table[First@Position[Rest@FoldList[#1-Mod[#1, #2]&, i, Range[2, i+1]], 0], {i, 30}] (* Birkas Gyorgy, Feb 26 2011 *)
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PROG
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(PARI) a(n)=if(n<1, 0, s=n; c=1; while(s-s%c>0, s=s-s%c; c++); c)
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CROSSREFS
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Cf. A140060, A140061.
Sequence in context: A071868 A179390 A237819 * A139789 A000720 A230980
Adjacent sequences: A082444 A082445 A082446 * A082448 A082449 A082450
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KEYWORD
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nonn
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AUTHOR
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Benoit Cloitre, Apr 25 2003
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STATUS
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approved
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