A084591 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...

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

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..54.

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, A084590, A084592, A084593.

Sequence in context: A191133 A050053 A272634 * A088758 A105176 A061937

Adjacent sequences: A084588 A084589 A084590 * A084592 A084593 A084594

Keyword

nonn

Author

Paul D. Hanna, Jun 04 2003

Status

approved