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A364650
Number of powers of 3 whose binary representation contains exactly n 1's.
2
1, 2, 1, 1, 1, 3, 0, 1, 1, 1, 2, 0, 1, 3, 1, 1, 2, 1, 1, 1, 0, 1
OFFSET
1,2
COMMENTS
Number of numbers k >= 0 such that A011754(k) = n.
Senge and Straus prove that a(n) is finite for all n.
After a(22), the sequence undoubtedly continues 0, 1, 3, 2, 1, 1, 1, 1, 0, 2, 1, 4, 1, 1, 0, 2, 4, 1, 2, 3, 0, 0, 2, 1, 1, 1, 1, 0, ..., but there seem to be proofs only for the first 22 terms (Dimitrov and Howe).
LINKS
Vassil S. Dimitrov and Everett W. Howe, Powers of 3 with few nonzero bits and a conjecture of Erdős, arXiv:2105.06440 [math.NT], 2021.
H. G. Senge and E. G. Straus, PV-numbers and sets of multiplicity, Periodica Mathematica Hungarica 3 (1973), 93-100.
EXAMPLE
There are a(6) = 3 powers of 3 that have exactly 6 binary 1's: 3^5 (11110011 in binary), 3^6 (1011011001), and 3^8 (1100110100001).
There is no power of 3 with exactly 7 binary 1's, so a(7) = 0.
CROSSREFS
Cf. A011754.
Sequence in context: A228239 A173749 A323618 * A246270 A265752 A125090
KEYWORD
nonn,base,more
AUTHOR
STATUS
approved