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

0,3

Comments

Periodic with period 63584 starting at n = 441329.

Links

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

Example

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.

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 *)

Prog

(Python 3)   # 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

Crossrefs

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

Sequence in context: A096116 A259431 A085875 * A302850 A338253 A060030

Adjacent sequences: A330612 A330613 A330614 * A330616 A330617 A330618

Keyword

nonn

Author

Jack Kiuttu, Dec 20 2019

Status

approved