cp's OEIS Frontend

A375529 Lexicographically earliest sequence of positive integers a(1), a(2), a(3), ... such that for any n > 0, Sum_{k = 1..n} prime(k)/a(k) < 1.

%I A375529 #36 Oct 20 2024 23:46:30
%S A375529 3,10,151,31711,1580159131,2950885219102973491,
%T A375529 11387023138265143513338462726052139311,
%U A375529 144918919004489964473283047921945994420315076260338720025368711042369934871
%N A375529 Lexicographically earliest sequence of positive integers a(1), a(2), a(3), ... such that for any n > 0, Sum_{k = 1..n} prime(k)/a(k) < 1.
%H A375529 Andrew Howroyd, <a href="/A375529/b375529.txt">Table of n, a(n) for n = 1..11</a>
%H A375529 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 A375529 a(n) = prime(n)*A375530(n-1) + 1.
%o A375529 (PARI) B(u)={my(v=vector(#u)); my(r=1); for(i=1, #u, my(t=floor(u[i]/r)+1); v[i]=t; r-=u[i]/t); v}
%o A375529 a(n)={B(vector(n,k,prime(k)))[n]} \\ _Andrew Howroyd_, Sep 04 2024
%Y A375529 Cf. A374663, A374983/A375516, A375530.
%K A375529 nonn
%O A375529 1,1
%A A375529 _Rémy Sigrist_ and _N. J. A. Sloane_, Sep 04 2024