A375791 a(n) = A375516(n+1) / A375516(n).

2, 2, 3, 4, 25, 201, 40201, 1212060151, 1305857607493406801, 1534737681943564047120326770001682121, 11777098761887521784975815904636471022877972047160405176265171997646882601

Offset

0,1

Links

Alois P. Heinz, Table of n, a(n) for n = 0..14

Example

a(7) = A375516(8) / A375516(7) = 11752718467440661200 / 9696481200 = 1212060151.

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-> denom(s(n+1))/denom(s(n)):
seq(a(n), n=0..10);  # Alois P. Heinz, Oct 19 2024

Mathematica

s[n_] := s[n] = If[n == 0, 0, s[n-1] + 1/(n*b[n])];
b[n_] := b[n] = 1 + Floor[1/((1 - s[n-1])*n)];
a[n_] := Denominator[s[n+1]]/Denominator[s[n]];
Table[a[n], {n, 0, 10}] (* Jean-François Alcover, Jul 02 2025, after Alois P. Heinz *)

Prog

(PARI) { r = 1; for (n = 1, 11, a = floor(1/(r*n))+1; d = denominator(r); r -= 1/(n*a); print1 (denominator(r)/d", "); ); }
(Python)
from itertools import count, islice
from math import gcd
def A375791_gen(): # generator of terms
    p, q = 0, 1
    for k in count(1):
        m = q//(k*(q-p))+1
        p, q = p*k*m+q, k*m*q
        p //= (r:=gcd(p, q))
        q //= r
        yield k*m//r
A375791_list = list(islice(A375791_gen(), 11)) # Chai Wah Wu, Aug 30 2024

Crossrefs

Cf. A374663, A375516.

Sequence in context: A022405 A309895 A361246 * A270744 A093927 A067088

Adjacent sequences: A375788 A375789 A375790 * A375792 A375793 A375794

Keyword

nonn

Author

Rémy Sigrist and N. J. A. Sloane, Aug 29 2024

Status

approved