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 A249482 Numbers n such that the summatory Liouville function L(n) (A002819) is zero and L(n-1)*L(n+1) = -1. 1
 2, 906150256, 906150308, 906150310, 906151576, 906154582, 906154586, 906154604, 906154606, 906154608, 906154758, 906154762, 906154764, 906154768, 906154770, 906154788, 906154794, 906154824, 906154826, 906154828, 906154830, 906154836, 906154838, 906154856 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS To create the data, the author studied the b-file of Donovan Johnson in A189229. For k>=1, in the interval [a(2k-1), a(2k)], L(n)<=0, in the interval [a(2k), a(2k+1)], L(n)>=0. In particular, for k=1, in the interval [2, 906150256], L(n)<=0. 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. LINKS P. Borwein, R. Ferguson, and M. Mossinghoff, Sign changes in sums of the Liouville function, Mathematics of Computation 77 (2008), pp. 1681-1694. M. Tanaka, A Numerical Investigation on Cumulative Sum of the Liouville Function, Tokyo J. Math. 3, 187-189, 1980. Eric Weisstein's World of Mathematics, Liouville Function Eric Weisstein's World of Mathematics, Polya Conjecture CROSSREFS Cf. A002819, A028488, A051470, A189229, A249487, A253174. Sequence in context: A034251 A230562 A170999 * A214600 A325175 A306499 Adjacent sequences:  A249479 A249480 A249481 * A249483 A249484 A249485 KEYWORD nonn AUTHOR Vladimir Shevelev, Jan 13 2015 STATUS approved

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Last modified December 12 15:11 EST 2019. Contains 329960 sequences. (Running on oeis4.)