A358055 a(n) is the least m such that A358052(m,k) = n for some k.

1, 2, 5, 8, 14, 20, 32, 38, 59, 59, 63, 116, 122, 158, 158, 218, 278, 278, 402, 548, 642, 642, 642, 642, 642, 1062, 1062, 1668, 2474, 2690, 2690, 2690, 2690, 2690, 3170, 3170, 3170, 3170, 3170, 3170, 3170, 9260, 9260, 9260, 9788, 9788, 11772, 11942, 11942, 11942, 11942, 11942

Offset

1,2

Comments

a(n) is the least m such that iteration of the map x -> floor(m/x) + (m mod x), starting at some k in [1,m], produces n distinct values before repeating.

Links

Table of n, a(n) for n=1..52.

Example

a(4) = 8 because A358052(8,6) = 4 and this is the first appearance of 4 in A358052.
Thus the map x -> floor(8/x) + (8 mod x) starting at 6 produces 4 distinct values before repeating: 6 -> 3 -> 4 -> 2 -> 4.

Maple

f:= proc(n, k) local x, S, count;
  S:= {k};
  x:= k;
  for count from 1 do
     x:= iquo(n, x) + irem(n, x);
     if member(x, S) then return count fi;
     S:= S union {x};
  od
end proc:
V:= Vector(50): count:= 0:
for n from 1 while count < 50 do
  for k from 1 to n do
    v:= f(n, k);
    if v <= 50 and V[v] = 0 then
       V[v]:= n; count:= count+1;
    fi
od od:
convert(V, list);

Mathematica

f[n_, k_] := Module[{x, S, count}, S = {k}; x = k; For[count = 1, True, count++, x = Quotient[n, x] + Mod[n, x]; If[MemberQ[S, x], Return@count]; S = S~Union~{x}]];
V = Table[0, {vmax = 40}]; count = 0;
For[n = 1, count < vmax, n++, For[k = 1, k <= n, k++, v = f[n, k]; If[v <= vmax && V[[v]] == 0, Print[n]; V[[v]] = n; count++]]];
V (* Jean-François Alcover, Mar 12 2024, after Maple code *)

Crossrefs

Cf. A234575, A358052.

Sequence in context: A006918 A274523 A165189 * A011842 A000094 A182377

Adjacent sequences: A358052 A358053 A358054 * A358056 A358057 A358058

Keyword

nonn

Author

J. M. Bergot and Robert Israel, Oct 27 2022

Status

approved