OFFSET
0,2
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).
LINKS
Yancheng Lu, Pascal program for sequence
Minecraft Wiki, Execute command
EXAMPLE
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]
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
CROSSREFS
KEYWORD
nonn
AUTHOR
Yancheng Lu, Mar 22 2019
STATUS
approved