A308818 a(n) = a(a(n-1) mod n) + a(a(n-2) mod n) with a(0)=2 and a(1)=3.

2, 3, 5, 7, 10, 7, 13, 15, 22, 23, 12, 6, 15, 18, 13, 25, 41, 37, 10, 22, 17, 40, 47, 40, 81, 38, 22, 53, 85, 134, 51, 29, 156, 215, 23, 47, 46, 35, 69, 98, 144, 81, 108, 116, 102, 37, 47, 37, 72, 75, 85, 104, 217, 111, 10, 15, 37, 60, 40, 147, 197, 51, 110

Offset: 0

Author

Arran Ireland, Jun 26 2019

Keywords

• nonn

Comments

a(0) and a(1) are chosen to be the smallest starting numbers greater than 1 that are believed to result in a sequence that doesn't cycle.

Empirical observation of the first 10^8 terms suggests that the sequence doesn't enter a cycle.

Conjectures: (i) This sequence doesn't enter a cycle. (ii) There is an integer greater than 1 that can never appear in this sequence.

Examples

			a(2) = a(a(2-1) mod 2) + a(a(2-2) mod 2) = a(a(1) mod 2) + a(a(0) mod 2) = a(3 mod 2) + a(2 mod 2) = a(1) + a(0) = 3 + 2 = 5.
		

Crossrefs

Cf. A005185, A046698, A003160.

Cf. A000027 (if a(0)=1 and a(1)=2).

Programs

Python

a = [2, 3]
for n in range(2, 10**4 + 3):
    a.append(a[(a[n - 1] % n)] + a[(a[n - 2] % n)])
    print((n - 2), ",", a[n - 2], sep="")