A074636 Define b(k) by the recursion b(1)=n, b(k+1)=b(k)-floor(k/b(k)). Sequence gives the value a(n) such that b(a(n))=0; if k>a(n) then b(k) is undefined.

2, 5, 5, 100, 17, 12, 100, 204, 171, 34, 46, 19, 204, 176, 80, 80, 286, 28, 30, 286, 46, 100, 204, 80, 100, 80, 100, 49, 323, 171, 101, 286, 51, 2546, 171, 100, 171, 904, 176, 904, 108, 204, 130, 204, 323, 230, 74, 61305, 160, 286, 286, 132, 176, 83, 99, 96

Offset

1,1

Comments

By definition a(n)>n. Conjecture: a(n) is always defined. Sometimes the b sequences for two values of n merge and a(n) is the same for both values. So some numbers, such as 100, 171 and 323, occur in the sequence more often than others.

Links

Robert Israel, Table of n, a(n) for n = 1..2000

Maple

f:= proc(n) local b, k;
  b[1]:= n;
  for k from 1 do
    b[k+1]:= b[k] - floor(k/b[k]);
    if b[k+1] = 0 then return k+1 fi;
  od;
end proc:
map(f, [$1..100]); # Robert Israel, Nov 13 2024

Mathematica

a[n_] := Module[{k, b}, For[k=0; b=n, b!=0, k++, b-=Floor[k/b]]; k]

Crossrefs

Cf. A073339.

Sequence in context: A271222 A073339 A180092 * A368388 A127598 A196550

Adjacent sequences: A074633 A074634 A074635 * A074637 A074638 A074639

Keyword

nonn,look

Author

Benoit Cloitre, Aug 25 2002

Extensions

Edited by Dean Hickerson, Aug 26 2002

Status

approved