STATUS
reviewed
approved
The OEIS is supported by the many generous donors to the OEIS Foundation.
Revision History for A075827
(Bold, blue-underlined text is an addition; faded, red-underlined text is aShowing entries 1-10 | older changes
Let u(1) = x and u(n+1) = (n^2/u(n)) + 1 for n >= 1; then a(n) is such that u(n) =(a(n)*x + b(n))/(c(n)*x + d(n)) (in lowest terms) and a(n), b(n), c(n), d(n) are positive integers.
(history; published version)
(history; published version)
STATUS
proposed
reviewed
STATUS
editing
proposed
LINKS
Petros Hadjicostas, <a href="/A075829/a075829.pdf">Proofs of various results about the sequence u(n)</a>, 2020.
STATUS
proposed
editing
STATUS
editing
proposed
FORMULA
From Petros Hadjicostas, May 18 2020: (Start)
Conjecture: a(n) = A024167(n)/gcd(A024167(n), A024167(n-1)) = A024167(n)/A334958(n-1) for n >= 2. (Cf. Michael Somos's result for d = A075829 using A024168.) - _Petros Hadjicostas_, May 06 2020
u(n) = (A024167(n)*x + A024168(n))/(A024167(n-1)*x + A024168(n-1)) for n >= 2. (End)
STATUS
proposed
editing
STATUS
editing
proposed
COMMENTS
For x real <> 0, 1 - 1/log(2), Lim_{n -> infinity} abs(u(n) - n) = abs((x - 1)/(1 + (x - 1)*log(2))). [Corrected by _Petros Hadjicostas_, May 18 2020]
STATUS
approved
editing
STATUS
proposed
approved