A365342 Positions of records in A087704.

2, 5, 10, 82, 284, 680, 1322, 68104, 149795, 213895, 1023127, 3775307, 25396927, 36254395, 53343289, 68677522, 266888359, 366901277, 558829814, 1576699732, 8527370677, 11616255230, 16948492520, 167299409017, 222801579737, 2001199132825, 5024272986979, 7880897129684

Offset

1,1

Comments

Numbers k such that iteration of the map x -> (5/3)*floor(x) starting at x = k takes more steps to reach an integer > k than it does for any number from 2 to k - 1.

Links

Table of n, a(n) for n=1..28.

Formula

A087704(a(n)) = A365343(n).

Example

a(3) = 10 is a term because A087704(10) = 9 and A087704(k) < 9 for 2 <= k < 10.

Maple

g:= x -> 5/3 * floor(x):
h:= proc(n) local i, k;
  k:= g(n);
  for i from 1 while not (k::integer and k > n) do k:= g(k) od:
  i
end proc:
M:= 2: A:= 2: count:= 1:
for n from 3 while count < 17  do
  v:= h(n);
  if v > M then count:= count+1; A:= A, n; M:= v fi;
od:
A;

Mathematica

g =  5/3 * Floor[#]&;
h[n_] := Module[{i, k}, k = g[n]; For[i = 1, !IntegerQ[k] && k > n, i++,  k = g[k]]; i];
M = 2; A = {2}; count = 1;
For[n = 3, count < 17, n++, v = h[n]; If[v > M, count++; A = Append[A, n]; Print[A]; M = v]];
A (* Jean-François Alcover, Sep 14 2023, after Robert Israel *)

Crossrefs

Cf. A087704, A365343.

Sequence in context: A018615 A082842 A018648 * A018670 A018704 A018751

Adjacent sequences: A365339 A365340 A365341 * A365343 A365344 A365345

Keyword

nonn

Author

Robert Israel, Sep 01 2023

Extensions

a(18)-a(21) from Chai Wah Wu, Sep 02 2023

a(22)-a(28) from Martin Ehrenstein, Sep 03 2023

Status

approved