This site is supported by donations to The OEIS Foundation.



Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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)



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.


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. 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


Cf. A002819, A028488, A051470, A189229, A249487, A253174.

Sequence in context: A034251 A230562 A170999 * A214600 A325175 A306499

Adjacent sequences:  A249479 A249480 A249481 * A249483 A249484 A249485




Vladimir Shevelev, Jan 13 2015



Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

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