A084816 Least integers that satisfy sum(n>0,1/a(n)^z)=0, where a(1)=1, a(n+1)>a(n) and z=I*2.

1, 3, 6, 13, 39, 131, 448, 1547, 5352, 18524, 64125, 221990, 768506, 2660499, 9210416, 31885663, 110385418, 382144818, 1322952481

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.

Links

Table of n, a(n) for n=1..19.

Formula

Limit a(n+1)/a(n) --> 3.4619139...

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. A084812-A084815, A084817-A084818.

Sequence in context: A216999 A036781 A370208 * A055738 A301656 A359669

Adjacent sequences: A084813 A084814 A084815 * A084817 A084818 A084819

Keyword

nonn

Author

Paul D. Hanna, Jun 04 2003

Status

approved