A292351 a(1) = a(2) = 1, a(3) = 3, a(4) = a(5) = 4; a(n) = a(n-a(n-1)) + a(n-a(n-2)) + a(n-a(n-3)) for n > 5.

1, 1, 3, 4, 4, 5, 7, 8, 6, 8, 10, 10, 10, 12, 11, 13, 13, 15, 14, 16, 16, 18, 18, 18, 21, 20, 18, 23, 21, 23, 24, 24, 20, 28, 28, 29, 20, 29, 30, 34, 27, 29, 31, 34, 35, 31, 33, 34, 39, 36, 34, 38, 38, 42, 36, 43, 39, 43, 42, 44, 42, 47, 43, 47, 48, 47, 46, 50, 50, 50, 48, 54, 53, 52, 52, 54, 60, 53, 55, 55, 63

Offset: 1

Author

Altug Alkan, Dec 12 2017

Keywords

• nonn

Comments

With five initial conditions, this sequence has the longest chaotic life for the recurrence a(n) = a(n-a(n-1)) + a(n-a(n-2)) + a(n-a(n-3)) where 1 <= a(i) <= 5 with 1 <= i <= 5. It is not known if this sequence is defined for all positive n. See plot of this sequence in Links section.

Links

• Hans Havermann, Scatterplot of a(n) for n <= 10^7

Crossrefs

Cf. A278055, A296413, A296440.

Programs

PARI

q=vector(10^5); q[1]=1; q[2]=1; q[3]=3; q[4]=4; q[5]=4; for(n=6, #q, q[n] = q[n-q[n-1]]+q[n-q[n-2]]+q[n-q[n-3]]); q

Scheme

;; With memoization-macro definec.
(definec (A292351 n) (cond ((<= n 2) 1) ((= 3 n) 3) ((<= n 5) 4) (else (+ (A292351 (- n (A292351 (- n 1)))) (A292351 (- n (A292351 (- n 2)))) (A292351 (- n (A292351 (- n 3)))))))) ;; Antti Karttunen, Dec 13 2017