A084799 - OEIS

A084799

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

%I #5 Mar 30 2012 18:36:38

%S 1,9,12,16,19,24,28,34,39,45,51,57,64,71,78,85,93,102,110,119,127,137,

%T 146,156,166,176,187,197,208,219,231,243,254,267,279,291,304,317,330,

%U 344,358,371,386,400,414,429,444,459,474,490,506,522,538,554,570,587

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

%C 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.

%C 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.

%o (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,","))

%Y Cf. A084588-A084593, A084800-A084810.

%K nonn

%O 1,2

%A _Paul D. Hanna_, Jun 04 2003