

A249482


Numbers n such that the summatory Liouville function L(n) (A002819) is zero and L(n1)*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
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OFFSET

1,1


COMMENTS

To create the data, the author studied the bfile of Donovan Johnson in A189229.
For k>=1,
in the interval [a(2k1), 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

Table of n, a(n) for n=1..24.
P. Borwein, R. Ferguson, and M. Mossinghoff, Sign changes in sums of the Liouville function, Mathematics of Computation 77 (2008), pp. 16811694.
M. Tanaka, A Numerical Investigation on Cumulative Sum of the Liouville Function, Tokyo J. Math. 3, 187189, 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



