A084815 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/4.

1, 15, 57, 226, 896, 3556, 14114, 56021, 222359, 882597, 3503247, 13905260, 55193448, 219076580, 869569671, 3451539247, 13700021484, 54378807610, 215843071542, 856735069788, 3400595509331, 13497813064840, 53576191885654, 212657289234917, 844089903986873

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 0.970295166... 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..25.

Prog

(PARI) my(z = I*Pi/4, 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, A084814, A084816, A084817, A084818.

Sequence in context: A336251 A158482 A184223 * A240152 A261419 A183942

Adjacent sequences: A084812 A084813 A084814 * A084816 A084817 A084818

Keyword

nonn

Author

Paul D. Hanna, Jun 04 2003

Extensions

a(8)-a(12) from Sean A. Irvine, May 11 2026

a(13) onward from Martin Fuller, May 24 2026

Status

approved