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%I #27 Feb 20 2023 03:15:11
%S 2,2,11,17,27,27,170,279,428,5879,5879,13871,13871,13871,41233,171707,
%T 1004646,1004646,1633357,5460156,11902755,21627159,21627159,38821328,
%U 41983357,179376463,179376463,179376463,179376463,179376463,179376463,179376463
%N a(n) is the smallest k such that the n consecutive values L(k), L(k+1), ..., L(k+n-1) = -1, where L(m) is the Liouville function A008836(m).
%C L(n) = (-1)^omega(n) where omega(n) is the number of prime factors of n with multiplicity.
%D H. Gupta, On a table of values of L(n), Proceedings of the Indian Academy of Sciences. Section A, 12 (1940), 407-409.
%D H. Gupta, A table of values of Liouville's function L(n), Research Bulletin of East Panjab University, No. 3 (Feb. 1950), 45-55.
%H Donovan Johnson and Giovanni Resta, <a href="/A175202/b175202.txt">Table of n, a(n) for n = 1..43</a> (terms < 10^13, first 38 terms from Donovan Johnson)
%H Peter Borwein, Ron Ferguson, and Michael J. Mossinghoff, <a href="http://dx.doi.org/10.1090/S0025-5718-08-02036-X">Sign changes in sums of the Liouville function</a>. Math. Comp. 77 (2008), 1681-1694.
%H R. S. Lehman, <a href="http://dx.doi.org/10.1090/S0025-5718-1960-0120198-5">On Liouville's function</a>, Math. Comp., 14 (1960), 311-320.
%e a(1) = 2 and L(2) = -1;
%e a(2) = 2 and L(2) = L(3)= -1;
%e a(3) = 11 and L(11) = L(12) = L(13) = -1;
%e a(4) = 17 and L(17) = L(18) = L(19) = L(20) = -1.
%p with(numtheory):for k from 0 to 30 do : indic:=0:for n from 1 to 1000000000 while (indic=0)do :s:=0:for i from 0 to k do :if (-1)^bigomega(n+i)= -1 then s:=s+1: else fi:od:if s=k+1 and indic=0 then print(n):indic:=1:else fi:od:od:
%t Table[k=1;While[Sum[LiouvilleLambda[k+i],{i,0,n-1}]!=-n,k++];k,{n,1,30}]
%Y Cf. A002819, A008836, A028488, A051470, A066794, A172354, A175201.
%K nonn
%O 1,1
%A _Michel Lagneau_, Mar 04 2010
%E a(15) and a(21) corrected by _Donovan Johnson_, Apr 01 2013
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