A308651 a(n+1) = k(a(n), n), where k(m, n) = (m*n) mod (m+n) and with a(1) = 5.

5, 5, 3, 3, 5, 5, 8, 11, 12, 3, 4, 14, 12, 6, 4, 3, 10, 8, 14, 2, 18, 27, 6, 22, 22, 33, 32, 38, 8, 10, 20, 8, 16, 38, 68, 11, 20, 56, 60, 63, 48, 10, 4, 31, 14, 40, 34, 59, 50, 74, 104, 34, 48, 19, 4, 43, 32, 44, 2, 57, 27, 63, 31, 73, 14, 41, 31, 19, 74, 101, 59, 29, 68, 29, 86, 10, 72, 31, 20, 95, 75, 147, 146, 210, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset: 1

Author

Stefan Gog, Aug 23 2019

Keywords

• nonn
• easy

Programs

Mathematica

a[1] = 5; a[n_] := a[n] = Mod[a[n - 1] * (n - 1), a[n - 1] + n - 1]; Array[a, 100] (* Amiram Eldar, Aug 29 2019 *)

Python

def k(a,b):
    return (a*b)%(a+b)
a = [5]
for n in range(1, 100):
    a.append(k(a[-1], n))
print(a)

Formula

a(k) = 0 for k >= 85. - Jinyuan Wang, Aug 26 2019

5 is one of the first starting values that produces rather long sequence until collapses to zero.