A307074 - OEIS

%I #63 Sep 03 2021 20:56:24

%S 1,2,3,5,9,15,27,47,55,95,187,191,375,415,751,831,1503,1663,3007,3327,

%T 6639,7039,13279,14079,26559,28159,53119,56319,106239,112639,212479,

%U 225279,424959,450559,849919,901119,1699839,1802239,3399679,3604479,6799359,7208959

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

%C 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).

%H Yancheng Lu, <a href="/A307074/a307074.txt">Pascal program for sequence</a>

%H Minecraft Wiki, <a href="https://minecraft.gamepedia.com/Commands/execute">Execute command</a>

%e n  |a(n)| maps                         | exponents

%e ---+----+------------------------------+------------

%e 1  | 1  | 1                            | []

%e 2  | 2  | 1 -> 2                       | [0]

%e 3  | 3  | 1 -> 2 -> 3                  | [0,0]

%e 4  | 5  | 1 -> 2 -> 4 -> 5             | [0,1,0]

%e 5  | 9  | 1 -> 2 -> 4 -> 8 -> 9        | [0,1,1,0]

%e 6  | 15 | 1 -> 2 -> 6 -> 7 -> 14 -> 15 | [0,2,0,1,0]

%t (* To get more terms of the sequence, increase terms and maxx,

%t    and then set maxi=trunc(lb(maxx)) *)

%t maxi=16;maxx=65536;terms=10;

%t a = NestList[

%t   Function[list,

%t    DeleteDuplicates[

%t     Join[list,

%t      Flatten[Table[If[# + #^i <= maxx, # + #^i, 1], {i, 0, maxi}] & /@

%t        list]]]], {1}, terms];

%t b = Prepend[Table[Complement[a[[i + 1]], a[[i]]], {i, Length[a] - 1}],

%t    First[a]];

%t Min /@ b

%Y Cf. A307092.

%K nonn

%O 0,2

%A _Yancheng Lu_, Mar 22 2019