A364969 a(n) = a(a(n-1)) if n is even, a(n) is the number of times a(n-1) occurs in the sequence so far if n is odd, with a(1) = 1.

1, 1, 2, 1, 3, 2, 2, 1, 4, 1, 5, 3, 2, 1, 6, 2, 5, 3, 3, 2, 6, 2, 7, 2, 8, 1, 7, 2, 9, 4, 2, 1, 8, 1, 9, 4, 3, 2, 11, 5, 3, 2, 12, 3, 7, 2, 13, 2, 14, 1, 10, 1, 11, 5, 4, 1, 12, 3, 8, 1, 13, 2, 15, 6, 3, 2, 16, 2, 17, 5, 5, 3, 10, 1, 14, 1, 15, 6, 4, 1, 16, 2

Offset: 1

Author

Tanmaya Mohanty, Oct 23 2023

Keywords

• nonn

Comments

Conjecture: All positive integers appear in the sequence.

Examples

			a(1) = 1 (by definition).
a(2) = a(a(1)) = a(1) = 1 (2 is even).
a(3) = number of times a(2) occurs = number of times 1 occurs = 2 (3 is odd).
a(4) = a(a(3)) = a(2) = 1 (4 is even).
a(5) = number of times a(4) occurs = number of times 1 occurs = 3 (5 is odd).
a(6) = a(a(5)) = a(3) = 2 (6 is even).
		

Programs

PARI

lista(nn) = my(va = vector(nn)); va[1] = 1; for (n=2, nn, if (n%2, va[n] = #select(x->(x==va[n-1]), va), va[n] = va[va[n-1]]);); va; \\ Michel Marcus, Oct 23 2023