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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, 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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified May 14 19:53 EDT 2021. Contains 343903 sequences. (Running on oeis4.)