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Search: id:A091155
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| A091155 |
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Numbers n such that n - 2^k is square-free for all 1 <= 2^k < n. |
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1
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| 2, 3, 4, 7, 15, 23, 39, 63, 75, 87, 111, 135, 147, 159, 195, 219, 231, 255, 267, 315, 387, 399, 411, 423, 435, 447, 459, 495, 519, 567, 615, 663, 675, 699, 711, 735, 747, 759, 771, 819, 867, 915, 999, 1011, 1023, 1035, 1047, 1071, 1095, 1119, 1155, 1167, 1263
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Erdos conjectures that this sequence is infinite. It appears that n = 3 (mod 12) except for n = 2, 4, 7 and 23.
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REFERENCES
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R. K. Guy, Unsolved Problems in Number Theory, A19.
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LINKS
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T. D. Noe, Table of n, a(n) for n = 1..5000
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EXAMPLE
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39 is on the list because 38, 37, 35, 31, 23 and 7 are all square-free.
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MATHEMATICA
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Needs["NumberTheory`NumberTheoryFunctions`"]; a={}; Do[k=1; While[sf=SquareFreeQ[n-k]; sf&&2k<n, k=2k]; If[sf, AppendTo[a, n]], {n, 2000}]; a
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CROSSREFS
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Cf. A039669 (n such that n-2^k are all primes).
Sequence in context: A014251 A098010 A088533 this_sequence A027362 A068194 A134459
Adjacent sequences: A091152 A091153 A091154 this_sequence A091156 A091157 A091158
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KEYWORD
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nonn
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AUTHOR
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T. D. Noe (noe(AT)sspectra.com), Dec 23 2003
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