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A375521
a(n) is the numerator of Sum_{k = 1..n} 1 / (k*A375781(k)).
3
0, 1, 5, 14, 103, 1154, 1336333, 892896284279, 398631887241408183843479, 19863422690705846097977473796903171171326157279, 14091270035344566960604487534521565339065390839583445590118556137472614250693240040301050079
OFFSET
0,3
LINKS
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]
EXAMPLE
The first few fractions are 0/1, 1/2, 5/6, 14/15, 103/105, 1154/1155, 1336333/1336335, 892896284279/892896284280, ...
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
PROG
(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
CROSSREFS
Sequence in context: A077262 A184439 A370006 * A316233 A317154 A283785
KEYWORD
nonn,frac,changed
AUTHOR
EXTENSIONS
a(0)=0 prepended by Alois P. Heinz, Oct 18 2024
STATUS
approved