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A278586
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Start with X = n^2. Repeatedly replace X with X - ceiling(X/n); a(n) is the number of steps to reach 0.
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9
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1, 3, 5, 8, 11, 14, 17, 21, 24, 28, 32, 36, 40, 44, 49, 53, 57, 62, 66, 71, 75, 80, 84, 90, 94, 99, 103, 109, 113, 118, 123, 128, 133, 139, 143, 149, 154, 159, 164, 170, 175, 180, 185, 191, 196, 201, 207, 212, 217, 223, 229, 234, 240, 246, 251, 256, 262, 268, 273, 279, 284, 290, 296, 302, 308
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OFFSET
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1,2
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LINKS
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MAPLE
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local x, a;
x := n^2 ;
a := 0 ;
while x <> 0 do
x:= x-ceil(x/n) ;
a := a+1 ;
end do:
a;
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MATHEMATICA
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f[n_] := Length@ NestWhileList[# - Ceiling[#/n] &, n^2, # > 1 &]; Array[f, 65] (* Robert G. Wilson v, Dec 01 2016 *)
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PROG
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(Magma) a:=[]; for n in [1..58] do k:=n^2; count:=0; while k gt 0 do count+:=1; k-:=Ceiling(k/n); end while; a[n]:=count; end for; a; // Jon E. Schoenfield, Dec 01 2016
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane, Dec 02 2016, based on discussions about the Pythagoras article in the Sequence Fans Mailing List, Dec 01 2016. Jack Brennen provided the definition given here.
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STATUS
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approved
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