

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
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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



STATUS

approved



