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Search: id:A069545
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| A069545 |
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Liouville clusters: the number of successive occurrences of signs in Liouville function lambda(k); a(2n-1) is number of successive positive signs, while a(2n) is number of successive negative signs. |
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1
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| 1, 2, 1, 1, 1, 2, 2, 3, 3, 4, 2, 1, 3, 6, 4, 1, 3, 5, 1, 2, 1, 1, 1, 2, 5, 1, 1, 1, 1, 1, 2, 3, 1, 4, 1, 2, 1, 3, 2, 1, 5, 1, 2, 1, 4, 2, 2
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Related open questions. What is the limit of ratio: a(n)/n, as n->infinity? What is frequency distribution of integer k in the sequence; a(n)=k for what set of n?
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REFERENCES
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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.
R. S. Lehman, On Liouville's function, Math. Comp., 14 (1960), 311-320.
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LINKS
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MathWorld, Liouville function
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FORMULA
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Related to summatory Liouville function (A002819): L(m)=sum_{k=1, n} (-1)^(k-1)*a(k) where m=sum_{k=1, n} a(k).
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EXAMPLE
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a(6)=2 because the 6-th Liouville cluster consists of 2 successive negative signs: lambda(7)=lambda(8)=(-1)
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CROSSREFS
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Cf. A008836, A002819, A001222, A028260, A026424.
Sequence in context: A059111 A103502 A127950 this_sequence A122520 A058393 A131256
Adjacent sequences: A069542 A069543 A069544 this_sequence A069546 A069547 A069548
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KEYWORD
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easy,nice,nonn
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Apr 17 2002
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