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A376050 Lexicographically earliest sequence of positive integers a(1), a(2), a(3), ... such that for any n > 0, S(n) = Sum_{k = 1..n} 1/((2*k-1)*a(k)) < 1.

%I A376050 #16 Oct 14 2024 00:10:21
%S A376050 2,1,2,3,6,172,137534,106557767317,10018727448950607892211,
%T A376050 218107864753736742334588510315735629277159621,
%U A376050 43040465365773907074907163986022284668974202910116417170603263409796800986397420975160781
%N A376050 Lexicographically earliest sequence of positive integers a(1), a(2), a(3), ... such that for any n > 0, S(n) = Sum_{k = 1..n} 1/((2*k-1)*a(k)) < 1.
%C A376050 It appears that S(n) = (e(n)-1)/e(n) for all n != 4, where e(n) = A376051(n). Exceptionally, S(4) = (e(4)-2)/e(4).
%C A376050 a(15) has 1420 decimal digits, too large for a b-file. - _Robert Israel_, Oct 13 2024
%D A376050 Rémy Sigrist and N. J. A. Sloane, Dampening Down a Divergent Series, Manuscript in preparation, September 2024.
%H A376050 Robert Israel, <a href="/A376050/b376050.txt">Table of n, a(n) for n = 1..14</a>
%p A376050 S:= 1:R:= NULL:
%p A376050 for i from 1 to 11 do
%p A376050   r:= ceil(1/((2*i-1)*S));
%p A376050   if r *(2*i-1) = 1/S then r:= r+1 fi;
%p A376050   R:= R,r;
%p A376050   S:= S - 1/((2*i-1)*r)
%p A376050 od:
%p A376050 R; # _Robert Israel_, Oct 13 2024
%Y A376050 Cf. A374663, A375516, A375531, A375532, A375781, A375522, A376048, A376049, A376051.
%K A376050 nonn,base
%O A376050 1,1
%A A376050 _N. J. A. Sloane_, Sep 13 2024