A084590 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...

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

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.

Links

Table of n, a(n) for n=1..52.

Andrew M. Odlyzko, The first 100 (nontrivial) zeros of the Riemann Zeta function.

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

Cf. A084588, A084589, A084591, A084592, A084593.

Sequence in context: A317811 A046461 A375268 * A279920 A041135 A041379

Adjacent sequences: A084587 A084588 A084589 * A084591 A084592 A084593

Keyword

nonn

Author

Paul D. Hanna, Jun 04 2003

Status

approved