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%I #21 Jan 15 2015 10:19:29
%S 2,906150256,906150308,906150310,906151576,906154582,906154586,
%T 906154604,906154606,906154608,906154758,906154762,906154764,
%U 906154768,906154770,906154788,906154794,906154824,906154826,906154828,906154830,906154836,906154838,906154856
%N Numbers n such that the summatory Liouville function L(n) (A002819) is zero and L(n-1)*L(n+1) = -1.
%C To create the data, the author studied the b-file of _Donovan Johnson_ in A189229.
%C For k>=1,
%C in the interval [a(2k-1), a(2k)], L(n)<=0,
%C in the interval [a(2k), a(2k+1)], L(n)>=0.
%C In particular, for k=1, in the interval [2, 906150256], L(n)<=0.
%C G. Polya (1919) conjectured that L(n)<=0, for n>=2. But this was disproved in 1958 by B. Haselgrove, and in 1980 M. Tanaka found the smallest counterexample, a(2)+1 = 906150257.
%H P. Borwein, R. Ferguson, and M. Mossinghoff, <a href="http://dx.doi.org/10.1090/S0025-5718-08-02036-X">Sign changes in sums of the Liouville function</a>, Mathematics of Computation 77 (2008), pp. 1681-1694.
%H M. Tanaka, <a href="http://dx.doi.org/10.3836/tjm/1270216093">A Numerical Investigation on Cumulative Sum of the Liouville Function</a>, Tokyo J. Math. 3, 187-189, 1980.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/LiouvilleFunction.html">Liouville Function</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PolyaConjecture.html">Polya Conjecture</a>
%Y Cf. A002819, A028488, A051470, A189229, A249487, A253174.
%K nonn
%O 1,1
%A _Vladimir Shevelev_, Jan 13 2015
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