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Search: id:A084590
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| A084590 |
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Least positive integers, all distinct, that satisfy sum(n>0,1/a(n)^z)=0, where z is the third nontrivial zero of the Riemann Zeta function: z=(1/2 + i*y) with y=25.01085758014568876321379099... |
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+0
3
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| 1, 3, 4, 7, 38, 56, 64, 72, 80, 89, 99, 110, 123, 138, 154, 171, 189, 208, 228, 249, 271, 295, 322, 352, 384, 418, 454, 493, 534, 577, 622, 669, 719, 771, 825, 881, 939, 1000, 1063, 1129, 1197, 1267, 1340, 1415, 1493, 1574, 1657, 1743, 1831, 1921, 2014, 2109
(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.
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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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Cf. A084588-A084589, A084591-A084593.
Sequence in context: A042773 A042173 A046461 this_sequence A041135 A041379 A134471
Adjacent sequences: A084587 A084588 A084589 this_sequence A084591 A084592 A084593
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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 04 2003
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