login
a(n) = A375516(n+1) / A375516(n).
2

%I #12 Oct 19 2024 21:07:12

%S 2,2,3,4,25,201,40201,1212060151,1305857607493406801,

%T 1534737681943564047120326770001682121,

%U 11777098761887521784975815904636471022877972047160405176265171997646882601

%N a(n) = A375516(n+1) / A375516(n).

%H Alois P. Heinz, <a href="/A375791/b375791.txt">Table of n, a(n) for n = 0..14</a>

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

%p s:= proc(n) s(n):= `if`(n=0, 0, s(n-1)+1/(n*b(n))) end:

%p b:= proc(n) b(n):= 1+floor(1/((1-s(n-1))*n)) end:

%p a:= n-> denom(s(n+1))/denom(s(n)):

%p seq(a(n), n=0..10); # _Alois P. Heinz_, Oct 19 2024

%o (PARI) { r = 1; for (n = 1, 11, a = floor(1/(r*n))+1; d = denominator(r); r -= 1/(n*a); print1 (denominator(r)/d", ");); }

%o (Python)

%o from itertools import count, islice

%o from math import gcd

%o def A375791_gen(): # generator of terms

%o p, q = 0, 1

%o for k in count(1):

%o m = q//(k*(q-p))+1

%o p, q = p*k*m+q, k*m*q

%o p //= (r:=gcd(p,q))

%o q //= r

%o yield k*m//r

%o A375791_list = list(islice(A375791_gen(),11)) # _Chai Wah Wu_, Aug 30 2024

%Y Cf. A374663, A375516.

%K nonn

%O 0,1

%A _Rémy Sigrist_ and _N. J. A. Sloane_, Aug 29 2024