A330615 a(0) = 1; a(1) = 1; a(n) = a(a(n - 1) mod n) + a(a(n - 2) mod n).

1, 1, 2, 3, 5, 4, 9, 7, 8, 15, 12, 6, 10, 21, 19, 14, 22, 23, 9, 20, 16, 38, 44, 52, 21, 40, 57, 24, 22, 65, 48, 26, 79, 78, 18, 17, 32, 102, 136, 41, 23, 53, 58, 26, 76, 83, 150, 47, 56, 54, 14, 22, 63, 56, 17, 24, 44, 97, 117, 253, 118, 112, 58, 171, 143, 74

Offset: 0

Author

Jack Kiuttu, Dec 20 2019

Keywords

• nonn

Comments

Periodic with period 63584 starting at n = 441329.

Examples

			n = 8: a(7) = 7, a(6) = 9, so a(8) = a(a(7) mod 8) + a(a(6) mod 8) = a(7 mod 8) + a(9 mod 8) = a(7) + a(1) = 7 + 1 = 8.
		

Links

• Jack Kiuttu, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A308818 (similar sequence with initial conditions a(0) = 2, a(1) = 3).

Programs

Mathematica

a[0] = a[1] = 1; a[n_] := a[n] = a[Mod[a[n-1], n]] + a[Mod[a[n-2], n]]; Array[a, 66, 0] (* Amiram Eldar, Dec 21 2019 *)

Python

# Lists terms up to given n.
def a_list(n):
   a=[1,1]
   for k in range(2,n+1):
      a.append(a[a[-1]%k]+a[a[-2]%k])
   return a