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A221281
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Numbers n such that lambda(n) = lambda(n+1) = lambda(n+2), where lambda(n) = A008836(n) is the Liouville function.
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3
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11, 14, 17, 18, 24, 27, 28, 29, 30, 33, 34, 38, 41, 42, 43, 54, 55, 56, 66, 70, 71, 78, 84, 85, 86, 93, 94, 97, 101, 107, 108, 112, 121, 132, 133, 134, 137, 140, 141, 142, 143, 144, 147, 158, 159, 162, 163, 170, 171, 172, 173, 174, 179, 180, 183, 190, 191, 201, 202, 203, 204
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OFFSET
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1,1
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COMMENTS
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Hildebrand proved that this sequence is infinite. More generally, he showed that the eight values (1, 1, 1), (1, 1, -1), ..., (-1, -1, -1) each appear infinitely often as consecutive values of the Liouville function.
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LINKS
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MATHEMATICA
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SequencePosition[LiouvilleLambda[Range[250]], {x_, x_, x_}][[All, 1]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jun 16 2021 *)
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PROG
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(PARI) is(n)=my(k=(-1)^bigomega(n)); k==(-1)^bigomega(n+1) && k==(-1)^bigomega(n+2)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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