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A377205 Lexicographically earliest sequence of positive integers a(1), a(2), ... such that for any n >= 0, s(n) = Sum_{k=1..n} 1/(k^2*a(k)) < 1.

%I A377205 #16 Oct 20 2024 14:14:29
%S A377205 2,1,1,1,1,1,3,9,171,122014,17661589931,412924014578486602517,
%T A377205 1248808068140660770289141544749321839183623,
%U A377205 4529027355107615424925871833487047912228337079416162414871862143803627237910792872226
%N A377205 Lexicographically earliest sequence of positive integers a(1), a(2), ... such that for any n >= 0, s(n) = Sum_{k=1..n} 1/(k^2*a(k)) < 1.
%H A377205 Alois P. Heinz, <a href="/A377205/b377205.txt">Table of n, a(n) for n = 1..17</a>
%e A377205 s(0), s(1), ... = 0, 1/2, 3/4, 31/36, 133/144, 3469/3600, 3569/3600, ... .
%p A377205 s:= proc(n) option remember; `if`(n=0, 0, s(n-1)+1/(n^2*a(n))) end:
%p A377205 a:= proc(n) option remember; 1+floor(1/((1-s(n-1))*n^2)) end:
%p A377205 seq(a(n), n=1..14);
%Y A377205 Cf. A000290, A013661, A374663, A377229, A377230.
%K A377205 nonn
%O A377205 1,1
%A A377205 _Alois P. Heinz_, Oct 19 2024