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.

3, 10, 151, 31711, 1580159131, 2950885219102973491, 11387023138265143513338462726052139311, 144918919004489964473283047921945994420315076260338720025368711042369934871

Offset: 1

Author

Rémy Sigrist and N. J. A. Sloane, Sep 04 2024

Keywords

• nonn

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..11
• N. J. A. Sloane, A Nasty Surprise in a Sequence and Other OEIS Stories, Experimental Mathematics Seminar, Rutgers University, Oct 10 2024, Youtube video; Slides [Mentions this sequence]

Crossrefs

Cf. A374663, A374983/A375516, A375530.

Programs

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}
a(n)={B(vector(n,k,prime(k)))[n]} \\ Andrew Howroyd, Sep 04 2024

Formula

a(n) = prime(n)*A375530(n-1) + 1.