A307074 a(n) is the smallest k such that A307092(k) = n.

1, 2, 3, 5, 9, 15, 27, 47, 55, 95, 187, 191, 375, 415, 751, 831, 1503, 1663, 3007, 3327, 6639, 7039, 13279, 14079, 26559, 28159, 53119, 56319, 106239, 112639, 212479, 225279, 424959, 450559, 849919, 901119, 1699839, 1802239, 3399679, 3604479, 6799359, 7208959

Offset: 0

Author

Yancheng Lu, Mar 22 2019

Keywords

• nonn

Comments

a(n) is the smallest number k such that exactly n iterations of the mapping x -> x + x^j, where j is a nonnegative integer, are required to reach x=k from x=1 (the j's in each iteration need not be identical).

Examples

			n  |a(n)| maps                         | exponents
---+----+------------------------------+------------
1  | 1  | 1                            | []
2  | 2  | 1 -> 2                       | [0]
3  | 3  | 1 -> 2 -> 3                  | [0,0]
4  | 5  | 1 -> 2 -> 4 -> 5             | [0,1,0]
5  | 9  | 1 -> 2 -> 4 -> 8 -> 9        | [0,1,1,0]
6  | 15 | 1 -> 2 -> 6 -> 7 -> 14 -> 15 | [0,2,0,1,0]
		

Links

• Yancheng Lu, Pascal program for sequence
• Minecraft Wiki, Execute command

Crossrefs

Cf. A307092.

Programs

Mathematica

(* To get more terms of the sequence, increase terms and maxx,
   and then set maxi=trunc(lb(maxx)) *)
maxi=16;maxx=65536;terms=10;
a = NestList[
  Function[list,
   DeleteDuplicates[
    Join[list,
     Flatten[Table[If[# + #^i <= maxx, # + #^i, 1], {i, 0, maxi}] & /@
       list]]]], {1}, terms];
b = Prepend[Table[Complement[a[[i + 1]], a[[i]]], {i, Length[a] - 1}],
   First[a]];
Min /@ b