A073339 Define b(k) by the recursion b(1)=n, b(k+1)=b(k)-trunc(k/b(k)), where trunc(x) is floor(x) for x>=0, ceiling(x) for x<0. Sequence gives the value a(n) such that b(a(n))=0; if k>a(n) then b(k) is undefined.

2, 5, 5, 69, 69, 12, 69, 69, 69, 29, 69, 19, 69, 69, 29, 29, 631, 28, 30, 631, 69, 69, 69, 631, 72, 42, 1167, 631, 72, 631, 631, 1167, 51, 631, 1167, 631, 631, 1167, 102, 103, 69, 1167, 1167, 69, 72, 631, 631, 631, 631, 1167, 631, 130, 631, 83, 631, 1167, 631

Offset

1,1

Comments

By definition a(n)>n. Conjecture: a(n) is always defined. Often the b sequences for two values of n merge and a(n) is the same for both values. So some numbers, such as 69, 631, 1167 and 689027, occur in the sequence more often than others.

Is sum(k=1,n,a(k))/(n^2*log(n)) bounded?

Links

Robert Israel, Table of n, a(n) for n = 1..1800

Maple

f:= proc(n) local b, k;
  b[1]:= n;
  for k from 1 do
    b[k+1]:= b[k] - trunc(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

trunc[x_] := If[x>0, Floor[x], Ceiling[x]]; a[n_] := Module[{k, b}, For[k=0; b=n, b!=0, k++, b-=trunc[k/b]]; k]

Crossrefs

Cf. A074636.

Sequence in context: A352392 A176081 A271222 * A180092 A074636 A368388

Adjacent sequences: A073336 A073337 A073338 * A073340 A073341 A073342

Keyword

nonn,look

Author

Benoit Cloitre, Aug 25 2002

Extensions

Edited by Dean Hickerson, Aug 26 2002

Status

approved