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%I #45 Dec 31 2023 00:50:05
%S 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,
%T 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,
%U 3,2,16,2,17,5,5,3,10,1,14,1,15,6,4,1,16,2
%N 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.
%C Conjecture: All positive integers appear in the sequence.
%e a(1) = 1 (by definition).
%e a(2) = a(a(1)) = a(1) = 1 (2 is even).
%e a(3) = number of times a(2) occurs = number of times 1 occurs = 2 (3 is odd).
%e a(4) = a(a(3)) = a(2) = 1 (4 is even).
%e a(5) = number of times a(4) occurs = number of times 1 occurs = 3 (5 is odd).
%e a(6) = a(a(5)) = a(3) = 2 (6 is even).
%o (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
%K nonn
%O 1,3
%A _Tanmaya Mohanty_, Oct 23 2023