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%I #14 Jun 16 2021 10:23:03
%S 11,14,17,18,24,27,28,29,30,33,34,38,41,42,43,54,55,56,66,70,71,78,84,
%T 85,86,93,94,97,101,107,108,112,121,132,133,134,137,140,141,142,143,
%U 144,147,158,159,162,163,170,171,172,173,174,179,180,183,190,191,201,202,203,204
%N Numbers n such that lambda(n) = lambda(n+1) = lambda(n+2), where lambda(n) = A008836(n) is the Liouville function.
%C 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.
%H Charles R Greathouse IV, <a href="/A221281/b221281.txt">Table of n, a(n) for n = 1..10000</a>
%H Adolf Hildebrand, <a href="http://dx.doi.org/10.5169/seals-55088">On consecutive values of the Liouville function</a>, Enseign. Math. (2) 32 (1986), no. 3-4, pp. 219-226.
%t SequencePosition[LiouvilleLambda[Range[250]],{x_,x_,x_}][[All,1]] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Jun 16 2021 *)
%o (PARI) is(n)=my(k=(-1)^bigomega(n)); k==(-1)^bigomega(n+1) && k==(-1)^bigomega(n+2)
%Y Subsequence of A221280. Cf. A008836, A221282.
%K nonn
%O 1,1
%A _Charles R Greathouse IV_, Jan 09 2013
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