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Search: id:A084588
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| A084588 |
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Least positive integers, all distinct, that satisfy sum(n>0,1/a(n)^z)=0, where z is the first nontrivial zero of the Riemann Zeta function: z=(1/2 + i*y) with y=14.13472514173469379045... |
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+0
7
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| 1, 2, 3, 4, 5, 6, 11, 13, 16, 20, 25, 30, 36, 44, 54, 65, 78, 93, 110, 130, 153, 178, 205, 234, 266, 300, 337, 376, 418, 462, 509, 559, 611, 666, 723, 783, 845, 910, 978, 1048, 1122, 1198, 1277, 1359, 1444, 1532, 1623, 1717, 1814, 1914, 2017, 2123, 2232, 2344
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Sequence satisfies: sum(n>0,1/a(n)^z)=0 by requiring that the modulus of the successive partial sums are monotonically decreasing in magnitude to zero for the given z.
Sequences A084588 - A084593 are related to zeros of the Riemann zeta function. The least integers that satisfy sum(n>0, 1/a(n)^z ) = 0, where a(1)=1, a(n+1)>a(n) and z is a nontrivial zero of the Riemann zeta function.
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LINKS
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Andrew M. Odlyzko, The first 100 (nontrivial) zeros of the Riemann Zeta function.
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PROGRAM
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(PARI) S=0; w=1; a=0; for(n=1, 100, b=a+1; while(abs(S+exp(-z*log(b)))>w, b++); S=S+exp(-z*log(b)); w=abs(S); a=b; print1(b, ", "))
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CROSSREFS
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Sequence in context: A108379 A082657 A108378 this_sequence A088411 A075073 A157420
Adjacent sequences: A084585 A084586 A084587 this_sequence A084589 A084590 A084591
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Jun 03 2003
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