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

Author

Robert Israel, Sep 01 2023

Keywords

• nonn

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.

Examples

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

Crossrefs

Cf. A087704, A365343.

Programs

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 *)

Formula

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

Extensions

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

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