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%I #20 Nov 24 2019 21:44:31
%S 1,1,1,2,2,3,3,3,4,4,5,5,5,6,6,7,7,8,8,8,8,9,9,10,10,11,11,12,12,13,
%T 13,13,13,13,14,14,15,15,16,16,17,17,18,18,19,19,20,20,20,21,21,21,21,
%U 21,21,22,22,23,23,24,24,25,25,26,26,27,27,28,28,29,29,30,30,31,31,32,32,32,33
%N a(n) = a(a(n-2)) + a(n-a(n-1)) with a(1) = a(2) = a(3) = 1.
%C A variation of the Hofstadter-Conway $10,000 sequence (A004001).
%C Similar with Newman generalization on A004001 (see A005350 and Kleitman's solution in Links section of A005350), a_i(n) is unbounded and slow sequence for all i >= 1 where a_i(n) = a_i(a_i(n-2)) + a_i(n-a_i(n-1)) with i + 1 initial conditions a_i(1) = a_i(2) = ... = a_i(i+1) = 1. In particular, a_1(n) = ceiling(n/2).
%H Altug Alkan, <a href="/A302128/a302128.pdf">Proof of slowness</a>
%F a(n+1) - a(n) = 0 or 1 for all n >= 1 and a(n) hits every positive integer.
%p a:=proc(n) option remember: if n<4 then 1 else procname(procname(n-2))+procname(n-procname(n-1)) fi; end: seq(a(n), n=1..100); # _Muniru A Asiru_, Jun 26 2018
%o (PARI) a=vector(99); for(n=1, 3, a[n] = 1); for(n=4, #a, a[n] = a[a[n-2]] + a[n-a[n-1]]); a
%o (GAP) a:=[1,1,1];; for n in [4..100] do a[n]:=a[a[n-2]]+a[n-a[n-1]]; od; a; # _Muniru A Asiru_, Jun 26 2018
%Y Cf. A004001, A005229, A005350.
%K nonn,easy
%O 1,4
%A _Altug Alkan_, Jun 20 2018
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