cp's OEIS Frontend

A376184 Lexicographically earliest sequence of positive integers a(1), a(2), a(3), ... such that for any n > 0, S(n) = Sum_{k = 1..n} b(k)/a(k) < 1, where {b(k)} is the sequence b(1)=5/4, b(2*i)=3/2, b(2*i+1)=6/5 (i>0).

%I A376184 #21 Jul 09 2025 05:06:00
%S A376184 2,5,17,341,92753,10753782821,92515075960384748177,
%T A376184 10698799099944699918936107506299150093941,
%U A376184 91571441744782016867976366392607084634231243149599342901251284090792487979854033
%N A376184 Lexicographically earliest sequence of positive integers a(1), a(2), a(3), ... such that for any n > 0, S(n) = Sum_{k = 1..n} b(k)/a(k) < 1, where {b(k)} is the sequence b(1)=5/4, b(2*i)=3/2, b(2*i+1)=6/5 (i>0).
%C A376184 This sequence and A376062 were discovered by Rémy Sigrist on Sep 09 2024. The two sequences {b(1)=7/6, b(k)=5/4 for k>1} and {b(1)=5/4, b(2*k)=3/2, b(2*k+1)=6/5 for k>0} are the first sequences {b(i)} discovered with the property that the sums S(n) do not converge to numbers of the form (e_n - 1)/e_n as n-> oo.
%H A376184 N. J. A. Sloane, <a href="https://www.youtube.com/watch?v=3RAYoaKMckM">A Nasty Surprise in a Sequence and Other OEIS Stories</a>, Experimental Mathematics Seminar, Rutgers University, Oct 10 2024, Youtube video; <a href="https://sites.math.rutgers.edu/~zeilberg/expmath/sloane85BD.pdf">Slides</a> [Mentions this sequence]
%e A376184 The initial values of S(n) are 5/8, 37/40, 677/680, 231877/231880, 21507565637/21507565640, 231287689900961870437/231287689900961870440, ...
%Y A376184 Cf. A004168, A082732, A374663, A375516, A375531, A375532, A375781, A375522, A376048-A376062, A376186.
%K A376184 nonn,base
%O A376184 1,1
%A A376184 _N. J. A. Sloane_, Sep 15 2024