|
|
A365215
|
|
Largest k such that the binary representation of 3^k has exactly n 1's, or -1 if no such k exists.
|
|
1
|
|
|
0, 2, 4, 3, 7, 8, -1, 9, 10, 12, 16, -1, 11, 18, 15, 24, 20, 25, 22, 21, -1, 23
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
Largest k such that A011754(k) = n, or -1 if no such k exists.
Senge and Straus prove that a(n) is finite for all n.
The first 22 terms are from Dimitrov and Howe (2021). After a(22), the sequence conjecturally but very likely continues -1, 26, 30, 32, 36, 40, 34, 27, -1, 39, 49, 45, 53, 38, -1, 47, 56, 57, 50, 58, -1, -1, 66, 51, 67, 59, 62, -1, ... .
|
|
LINKS
|
|
|
MATHEMATICA
|
LargestK[n_Integer] := Module[{k = 1000(*Assuming 1000 is large enough for the search. Adjust if necessary.*), binCount}, While[k >= 0, binCount = Total[IntegerDigits[3^k, 2]]; If[binCount == n, Return[k]]; k--; ]; -1]; Table[LargestK[n], {n, 22}] (* _Robert P. P. McKone_, Aug 26 2023 *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
sign,base,more
|
|
AUTHOR
|
_Pontus von Brömssen_, Aug 26 2023
|
|
STATUS
|
approved
|
|
|
|