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A307074
a(n) is the smallest k such that A307092(k) = n.
5
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
0,2
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).
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
Cf. A307092.
Sequence in context: A067847 A190138 A273905 * A293855 A022858 A301470
KEYWORD
nonn
AUTHOR
Yancheng Lu, Mar 22 2019
STATUS
approved