A375521 a(n) is the numerator of Sum_{k = 1..n} 1 / (k*A375781(k)).

0, 1, 5, 14, 103, 1154, 1336333, 892896284279, 398631887241408183843479, 19863422690705846097977473796903171171326157279, 14091270035344566960604487534521565339065390839583445590118556137472614250693240040301050079

Offset: 0

Author

Rémy Sigrist and N. J. A. Sloane, Aug 30 2024

Keywords

• nonn
• frac

Examples

			The first few fractions are 0/1, 1/2, 5/6, 14/15, 103/105, 1154/1155, 1336333/1336335, 892896284279/892896284280, ...
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..13
• 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. A375781, A375522.

Programs

Maple

s:= proc(n) s(n):= `if`(n=0, 0, s(n-1)+1/(ithprime(n)*b(n))) end:
b:= proc(n) b(n):= 1+floor(1/((1-s(n-1))*ithprime(n))) end:
a:= n-> numer(s(n)):
seq(a(n), n=0..10);  # Alois P. Heinz, Oct 18 2024

Mathematica

s[n_] := s[n] = If[n == 0, 0, s[n - 1] + 1/(Prime[n]*b[n])];
b[n_] := b[n] = 1 + Floor[1/((1 - s[n - 1])*Prime[n])];
a[n_] := Numerator[s[n]];
Table[a[n], {n, 0, 10}] (* Jean-François Alcover, Apr 22 2025, after Alois P. Heinz *)

Python

from itertools import islice
from math import gcd
from sympy import nextprime
def A375521_gen(): # generator of terms
    p, q, k = 0, 1, 1
    while (k:=nextprime(k)):
        m=q//(k*(q-p))+1
        p, q = p*k*m+q, k*m*q
        p //= (r:=gcd(p,q))
        q //= r
        yield p
A375521_list = list(islice(A375521_gen(),11)) # Chai Wah Wu, Aug 30 2024

Extensions

a(0)=0 prepended by Alois P. Heinz, Oct 18 2024