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

1,1

Comments

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

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.

Example

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.

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}]

Crossrefs

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

Sequence in context: A194638 A327870 A235606 * A187430 A151365 A244280

Adjacent sequences: A175199 A175200 A175201 * A175203 A175204 A175205

Keyword

nonn

Author

Michel Lagneau, Mar 04 2010

Extensions

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

Status

approved