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Search: id:A084591
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| A084591 |
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Least positive integers, all distinct, that satisfy sum(n>0,1/a(n)^z)=0, where z is the fourth nontrivial zero of the Riemann Zeta function: z=(1/2 + i*y) with y=30.4248761258595132103118975... |
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+0
3
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| 1, 2, 4, 6, 7, 15, 20, 27, 37, 50, 55, 61, 67, 73, 80, 108, 118, 129, 141, 154, 168, 184, 202, 221, 241, 262, 284, 307, 331, 356, 383, 413, 446, 481, 518, 557, 598, 641, 687, 736, 788, 843, 901, 962, 1025, 1091, 1159, 1230, 1303, 1379, 1457, 1538, 1621, 1707
(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-A084590, A084592-A084593.
Sequence in context: A138398 A086781 A050053 this_sequence A088758 A105176 A061937
Adjacent sequences: A084588 A084589 A084590 this_sequence A084592 A084593 A084594
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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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