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A327466
Number of nonempty subsets of [1..n] which are geometric progressions with rational ratio and are locally maximal.
2
1, 1, 3, 4, 8, 13, 19, 23, 27, 36, 46, 55, 67, 80, 94, 103, 119, 132, 150, 167, 187, 208, 230, 250, 266, 291, 311, 336, 364, 393, 423, 447, 479, 512, 546
OFFSET
1,3
COMMENTS
"Locally maximal" subsets are those subsets in geometrical progression that cannot be extended to a larger subset of [1..n] in geometric progression. [Comment made precise by Giovanni Resta, Sep 30 2019.]
One might have expected that the GP would be required to have an integer ratio, but in fact we allow rational ratios. The GPs can be assumed to be strictly increasing. - N. J. A. Sloane, Oct 03 2019
EXAMPLE
Illustrations of some initial terms:
n=3: (12),(13),(23).
n=4: (124),(13),(23),(34).
n=8: (1248), plus all 28 pairs (ij) from [1..8] except the six subsets of (1248), so a(8) = 1 + 28 - 6 = 23.
MATHEMATICA
a[1] = 1; a[n_] := Block[{t = Select[ Subsets[ Range[n], {2, Ceiling[ Log2[n + 1]]}], Length@ Union[ Rest[#]/ Most[#]] == 1 &], i = 2}, t = Reverse@ SortBy[t, Length]; i=2; While[i <= Length[t], If[ AnyTrue[ Take[t, i-1], SubsetQ[#, t[[i]]] &], t = Delete[t, i]; i=2; Continue[], i++]]; Length@ t]; Array[a, 16] (* Giovanni Resta, Sep 30 2019 *)
CROSSREFS
See A327469 for GPs of length > 2.
Cf. A309095.
Sequence in context: A343562 A375420 A033955 * A049720 A078172 A022308
KEYWORD
nonn,more
AUTHOR
N. J. A. Sloane, Sep 29 2019
EXTENSIONS
a(9)-a(35) from Giovanni Resta, Sep 30 2019
STATUS
approved

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Last modified September 22 05:46 EDT 2024. Contains 376097 sequences. (Running on oeis4.)