A377230 - OEIS

%I #9 Oct 20 2024 14:13:51

%S 2,1,2,2,3,5,23,806,519065,220441054222,222723684271305542570701,

%T 41974171914555858099300698444579076459265512901,

%U 1510140949639448391630842209382251970116940997822995817347241840058937174456186756365141648201

%N Lexicographically earliest sequence of positive integers a(1), a(2), ... such that for any n >= 0, s(n) = Sum_{k=1..n} 1/(T(k)*a(k)) < 1, T = A000217.

%H Alois P. Heinz, <a href="/A377230/b377230.txt">Table of n, a(n) for n = 1..16</a>

%e s(0), s(1), ... = 0, 1/2, 5/6, 11/12, 29/30, 89/90, 629/630, ... .

%p T:= n-> n*(n+1)/2:

%p s:= proc(n) option remember; `if`(n=0, 0, s(n-1)+1/(T(n)*a(n))) end:

%p a:= proc(n) option remember; 1+floor(1/((1-s(n-1))*T(n))) end:

%p seq(a(n), n=1..13);

%Y Cf. A000217, A374663, A377205, A377229.

%K nonn

%O 1,1

%A _Alois P. Heinz_, Oct 20 2024