OFFSET
0,3
COMMENTS
For n = 1..36, Sum_{k = 1..n} 1 / (k*A374663(k)) = a(n) / (1 + a(n)). In fact this holds for all n >= 1.
LINKS
N. J. A. Sloane, Table of n, a(n) for n = 0..14
Rémy Sigrist, Proof of Theorem, Aug 26 2024, revised Sep 01 2024.
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
MAPLE
s:= proc(n) s(n):= `if`(n=0, 0, s(n-1)+1/(n*b(n))) end:
b:= proc(n) b(n):= 1+floor(1/((1-s(n-1))*n)) end:
a:= n-> numer(s(n)):
seq(a(n), n=0..10); # Alois P. Heinz, Oct 18 2024
PROG
(PARI) { print1 (0); t = 0; for (n = 1, 10, for (v = c=ceil(1/(n*(1-t))), oo, if (t + 1/(n*v) < 1, t += 1/(n*v); print1 (", " numerator(t)); break; ); ); ); }
(Python)
from itertools import count, islice
from math import gcd
def A374983_gen(): # generator of terms
p, q = 0, 1
for k in count(1):
yield p
m = q//(k*(q-p))+1
p, q = p*k*m+q, k*m*q
p //= (r:=gcd(p, q))
q //= r
CROSSREFS
KEYWORD
nonn,frac
AUTHOR
Rémy Sigrist, Aug 04 2024
STATUS
approved