Search: id:A084589
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%I A084589
%S A084589 1,2,3,4,5,6,7,8,12,18,49,55,62,94,105,118,134,153,173,194,217,243,272,
%T A084589 304,339,377,418,462,509,559,612,668,727,789,854,922,993,1067,1144,1224,
%U A084589 1307,1393,1482,1574,1669,1767,1868,1972,2080,2190,2304,2421,2541,2664
%N A084589 Least positive integers, all distinct, that satisfy sum(n>0,1/a(n)^z)=0, 
               where z is the second nontrivial zero of the Riemann Zeta function: 
               z=(1/2 + i*y) with y=21.022039638771554992628...
%C A084589 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.
%H A084589 Andrew M. Odlyzko, <a href="http://pi.lacim.uqam.ca/piDATA/zeta100.html">
               The first 100 (nontrivial) zeros of the Riemann Zeta function.</a>
%o A084589 (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,","))
%Y A084589 Cf. A084588, A084590-A084593.
%Y A084589 Sequence in context: A015845 A030702 A033087 this_sequence A165306 A032986 
               A032977
%Y A084589 Adjacent sequences: A084586 A084587 A084588 this_sequence A084590 A084591 
               A084592
%K A084589 nonn
%O A084589 1,2
%A A084589 Paul D. Hanna (pauldhanna(AT)juno.com), Jun 04 2003

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