A084592 Least positive integers, all distinct, that satisfy Sum_{n>0} 1/a(n)^z = 0, where z is the fifth nontrivial zero of the Riemann zeta function: z=(1/2 + i*y) with y=32.935061587739189690662368964...

1, 2, 4, 5, 20, 58, 64, 84, 91, 99, 108, 118, 129, 142, 156, 170, 185, 201, 219, 238, 257, 277, 299, 323, 348, 374, 402, 432, 463, 495, 529, 566, 606, 649, 695, 744, 796, 851, 909, 969, 1031, 1095, 1162, 1232, 1305, 1381, 1459, 1540, 1623, 1709, 1797, 1888

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: A056440 A101843 A192117 * A101587 A277853 A200906

Adjacent sequences: A084589 A084590 A084591 * A084593 A084594 A084595

Keyword

nonn

Author

Paul D. Hanna, Jun 04 2003

Status

approved