

A084588


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...


7



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
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OFFSET

1,2


COMMENTS

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.


LINKS



MATHEMATICA

Reap[For[z = ZetaZero[1]; S = 0; w = 1; a = 0; n = 1, n <= 100, n++, b = a + 1; While[Abs[S + Exp[z*Log[b]]] > w, b++]; S = S + Exp[z*Log[b]]; w = Abs[S]; a = b; Print[b]; Sow[b]]][[2, 1]] (* JeanFrançois Alcover, Oct 22 2019, from PARI *)


PROG

(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, ", "))


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



