cp's OEIS Frontend

A376062 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 {7/6, 5/4, 5/4, 5/4, ...}.

%I A376062 #17 Oct 20 2024 23:54:38
%S A376062 2,4,13,157,24493,599882557,359859081592975693,
%T A376062 129498558604939936868397356895854557,
%U A376062 16769876680757063368089314196389622249367851612542961252860614401811693
%N A376062 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 {7/6, 5/4, 5/4, 5/4, ...}.
%C A376062 This sequence and A376186 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.
%C A376062 This is essentially the same sequence as A004168 and A082732.
%H A376062 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]
%F A376062 a(n+1) = a(n)^2 - a(n) + 1 for n >= 2.
%t A376062 Join[{2}, RecurrenceTable[{a[n+1] == a[n]^2 - a[n] + 1, a[2] == 4}, a, {n, 2, 9}]] (* _Amiram Eldar_, Sep 15 2024 *)
%Y A376062 Cf. A004168, A082732, A374663, A375516, A375531, A375532, A375781, A375522, A376048-A376061, A376185.
%K A376062 nonn
%O A376062 1,1
%A A376062 _N. J. A. Sloane_, Sep 14 2024