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Search: id:A089510
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| A089510 |
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A periodic sequence with period length 30. |
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+0
1
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| 1, 0, 0, 0, 0, -1, 1, 0, 0, -1, 1, -1, 1, 0, -1, 0, 1, -1, 1, -1, 0, 0, 1, -1, 0, 0, 0, 0, 1, -1
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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a(n)=a(n+30) are the coefficients of S(x) := T(x)-T(x/2)-T(x/3)-T(x/5)+T(x/30) with Chebyshev's function T(x) := sum(ln(n),n=1..floor(x)), expanded in terms of psi(x/n) with psi(x) := ln(A003418(floor(x))) (logarithm of least common multiple of {1,2,...,floor(x)}): S(x)=sum(a(n)*psi(x/n),n=1..infinity).
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REFERENCES
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M. I. Bashmakov: On Bertrand's Conjecture, pp. 21-26 in: Kvant Selecta: Algebra and Analysis, I, ed. S. Tabachnikov, Am. Math. Soc., 1999
L. G. Limanov: On n! and the Number e (Several Approaches to a Certain Problem), pp. 57-64 in: Kvant Selecta: Algebra and Analysis, I, ed. S. Tabachnikov, Am. Math. Soc., 1999
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LINKS
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Eric Weisstein's World of Mathematics, Chebyshev Functions.
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FORMULA
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a(n)= 1-floor(2^(floor(n/2)-n/2)) - floor(2^(floor(n/3)-n/3)) - floor(2^(floor(n/5)-n/5)) + floor(2^(floor(n/30)-n/30)), from eq.(4), p. 64 of the Limanov reference.
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CROSSREFS
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Sequence in context: A011746 A123192 A071005 this_sequence A138885 A014065 A014049
Adjacent sequences: A089507 A089508 A089509 this_sequence A089511 A089512 A089513
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KEYWORD
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sign,easy
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AUTHOR
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Wolfdieter Lang (wolfdieter.lang_AT_physik_DOT_uni-karlsruhe_DOT_de), Dec 01 2003
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