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

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

Keywords

• nonn
• easy

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.

Crossrefs

Cf. A052488.

Programs

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

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 *)