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...

1, 2, 3, 4, 5, 6, 7, 8, 12, 18, 49, 55, 62, 94, 105, 118, 134, 153, 173, 194, 217, 243, 272, 304, 339, 377, 418, 462, 509, 559, 612, 668, 727, 789, 854, 922, 993, 1067, 1144, 1224, 1307, 1393, 1482, 1574, 1669, 1767, 1868, 1972, 2080, 2190, 2304, 2421, 2541, 2664

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.

Index entries for 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, A084590, A084591, A084592, A084593.

Sequence in context: A030702 A305926 A033087 * A271831 A180628 A165306

Adjacent sequences: A084586 A084587 A084588 * A084590 A084591 A084592

Keyword

nonn

Author

Paul D. Hanna, Jun 04 2003

Status

approved