A084799 Least positive integers, all distinct, that satisfy sum(n>0,1/a(n)^z)=0, where z=(3+I*4)/5.

1, 9, 12, 16, 19, 24, 28, 34, 39, 45, 51, 57, 64, 71, 78, 85, 93, 102, 110, 119, 127, 137, 146, 156, 166, 176, 187, 197, 208, 219, 231, 243, 254, 267, 279, 291, 304, 317, 330, 344, 358, 371, 386, 400, 414, 429, 444, 459, 474, 490, 506, 522, 538, 554, 570, 587

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 for the given z.

Sequences A084799 - A084804 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 = unit complex numbers using Pythagorean triples: (3+I*4)/5, (4+I*3)/5, (12+I*5)/13, (24+I*7)/25, (40+I*9)/41; these z produce a special pattern to the sequences.

Links

Table of n, a(n) for n=1..56.

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-A084593, A084800-A084810.

Sequence in context: A337701 A048699 A019468 * A166136 A120154 A084375

Adjacent sequences: A084796 A084797 A084798 * A084800 A084801 A084802

Keyword

nonn

Author

Paul D. Hanna, Jun 04 2003

Status

approved