A084814 Least integers that satisfy Sum_{n>=1} 1/a(n)^z = 0, where a(1)=1, a(n+1) > a(n) and z = i*Pi/2.

1, 4, 8, 17, 37, 82, 185, 419, 952, 2166, 4932, 11234, 25593, 58307, 132837, 302638, 689491, 1570849, 3578825, 8153546, 18576017, 42321270, 96419483, 219670083, 500468828, 1140205555, 2597701665, 5918278432, 13483465048, 30719039635, 69986416161, 159448293478

Offset

1,2

Comments

Sequence satisfies Sum_{n>=1} 1/a(n)^z = 0 by requiring that the modulus of the successive partial sums are monotonically decreasing in magnitude for the given z.

|Sum_{k=1..n} 1/a(k)^z| appears to converge geometrically to 0.829785815... Does this behavior continue? If this is true then the complex sum converges to a circular orbit rather than a single value. - Martin Fuller, May 24 2026

Links

Table of n, a(n) for n=1..32.

Prog

(PARI) my(z = I*Pi/2, 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, ", "))
(PARI) \\ See Fuller link in A084813

Crossrefs

Cf. A084812, A084813, A084815, A084816, A084817, A084818.

Sequence in context: A115618 A387224 A019479 * A098125 A335274 A296399

Adjacent sequences: A084811 A084812 A084813 * A084815 A084816 A084817

Keyword

nonn

Author

Paul D. Hanna, Jun 04 2003

Extensions

a(14)-a(21) from Sean A. Irvine, May 11 2026

a(22) onward from Martin Fuller, May 24 2026

Status

approved