A175202 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).

2, 2, 11, 17, 27, 27, 170, 279, 428, 5879, 5879, 13871, 13871, 13871, 41233, 171707, 1004646, 1004646, 1633357, 5460156, 11902755, 21627159, 21627159, 38821328, 41983357, 179376463, 179376463, 179376463, 179376463, 179376463, 179376463, 179376463

Offset: 1

Author

Michel Lagneau, Mar 04 2010

Keywords

• nonn

Comments

L(n) = (-1)^omega(n) where omega(n) is the number of prime factors of n with multiplicity.

Examples

			a(1) = 2 and L(2) = -1;
a(2) = 2 and L(2) = L(3)= -1;
a(3) = 11 and L(11) = L(12) = L(13) = -1;
a(4) = 17 and L(17) = L(18) = L(19) = L(20) = -1.
		

References

• H. Gupta, On a table of values of L(n), Proceedings of the Indian Academy of Sciences. Section A, 12 (1940), 407-409.
• H. Gupta, A table of values of Liouville's function L(n), Research Bulletin of East Panjab University, No. 3 (Feb. 1950), 45-55.

Links

• Donovan Johnson and Giovanni Resta, Table of n, a(n) for n = 1..43 (terms < 10^13, first 38 terms from Donovan Johnson)
• Peter Borwein, Ron Ferguson, and Michael J. Mossinghoff, Sign changes in sums of the Liouville function. Math. Comp. 77 (2008), 1681-1694.
• R. S. Lehman, On Liouville's function, Math. Comp., 14 (1960), 311-320.

Crossrefs

Cf. A002819, A008836, A028488, A051470, A066794, A172354, A175201.

Programs

Maple

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:

Mathematica

Table[k=1;While[Sum[LiouvilleLambda[k+i],{i,0,n-1}]!=-n,k++];k,{n,1,30}]

Extensions

a(15) and a(21) corrected by Donovan Johnson, Apr 01 2013