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

%I A307074 #63 Sep 03 2021 20:56:24
%S A307074 1,2,3,5,9,15,27,47,55,95,187,191,375,415,751,831,1503,1663,3007,3327,
%T A307074 6639,7039,13279,14079,26559,28159,53119,56319,106239,112639,212479,
%U A307074 225279,424959,450559,849919,901119,1699839,1802239,3399679,3604479,6799359,7208959
%N A307074 a(n) is the smallest k such that A307092(k) = n.
%C A307074 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 A307074 Yancheng Lu, <a href="/A307074/a307074.txt">Pascal program for sequence</a>
%H A307074 Minecraft Wiki, <a href="https://minecraft.gamepedia.com/Commands/execute">Execute command</a>
%e A307074 n  |a(n)| maps                         | exponents
%e A307074 ---+----+------------------------------+------------
%e A307074 1  | 1  | 1                            | []
%e A307074 2  | 2  | 1 -> 2                       | [0]
%e A307074 3  | 3  | 1 -> 2 -> 3                  | [0,0]
%e A307074 4  | 5  | 1 -> 2 -> 4 -> 5             | [0,1,0]
%e A307074 5  | 9  | 1 -> 2 -> 4 -> 8 -> 9        | [0,1,1,0]
%e A307074 6  | 15 | 1 -> 2 -> 6 -> 7 -> 14 -> 15 | [0,2,0,1,0]
%t A307074 (* To get more terms of the sequence, increase terms and maxx,
%t A307074    and then set maxi=trunc(lb(maxx)) *)
%t A307074 maxi=16;maxx=65536;terms=10;
%t A307074 a = NestList[
%t A307074   Function[list,
%t A307074    DeleteDuplicates[
%t A307074     Join[list,
%t A307074      Flatten[Table[If[# + #^i <= maxx, # + #^i, 1], {i, 0, maxi}] & /@
%t A307074        list]]]], {1}, terms];
%t A307074 b = Prepend[Table[Complement[a[[i + 1]], a[[i]]], {i, Length[a] - 1}],
%t A307074    First[a]];
%t A307074 Min /@ b
%Y A307074 Cf. A307092.
%K A307074 nonn
%O A307074 0,2
%A A307074 _Yancheng Lu_, Mar 22 2019