A278586 Start with X = n^2. Repeatedly replace X with X - ceiling(X/n); a(n) is the number of steps to reach 0.

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

Offset

1,2

Links

Robert G. Wilson v, Table of n, a(n) for n = 1..1000

Matthijs Coster, Een Eigen Rij - Uitslag Prijsvraag, Pythagoras, Number 6, June 2016, pp. 20-21. The sequence was discovered by Pim Spelier.

Maple

A278586 := proc(n)
    local x, a;
    x := n^2 ;
    a := 0 ;
    while x <> 0 do
        x:= x-ceil(x/n) ;
        a := a+1 ;
    end do:
    a;
end proc: # R. J. Mathar, Dec 02 2016

Mathematica

f[n_] := Length@ NestWhileList[# - Ceiling[#/n] &, n^2, # > 1 &]; Array[f, 65] (* Robert G. Wilson v, Dec 01 2016 *)

Prog

(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

Crossrefs

Cf. A052488.

Sequence in context: A102696 A130262 A094228 * A001855 A006591 A310027

Adjacent sequences: A278583 A278584 A278585 * A278587 A278588 A278589

Keyword

nonn,easy

Author

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.

Status

approved