OFFSET
1,3
COMMENTS
2 >= a(n) / a(n-1) > 0. Empirically the average growth rate is 1.32... in comparison to 1.618... (golden ratio).
a(n)^(1/n) tends to 1.228... - Vaclav Kotesovec, Jan 01 2020
LINKS
Vaclav Kotesovec, Plot of a(n)^(1/n) for n = 1..1000000
EXAMPLE
a(1) = 1; a(2) = 1; a(3) = 1/gcd(1,2) + 1/gcd(1,1) = 2; a(4) = 2/gcd(2,3) + 1/gcd(1,2) = 3 and so on.
MATHEMATICA
a[1] = a[2] = 1; a[n_] := a[n] = a[n - 1] / GCD[a[n - 1], n - 1] + a[n - 2] / GCD[a[n - 2], n - 2]; Array[a, 100] (* Amiram Eldar, Jan 01 2020 *)
PROG
(Magma) a:=[1, 1]; for n in [3..60] do Append(~a, a[n-1]/ Gcd(a[n-1], n-1) + a[n-2] / Gcd(a[n-2], n-2)); end for; a; // Marius A. Burtea, Jan 01 2020
(PARI) seq(n)={my(a=vector(n)); a[1]=a[2]=1; for(n=3, #a, a[n] = a[n-1]/gcd(a[n-1], n-1) + a[n-2]/gcd(a[n-2], n-2)); a} \\ Andrew Howroyd, Jan 01 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
Ctibor O. Zizka, Jan 01 2020
STATUS
approved