%I #6 Nov 29 2023 11:43:29
%S 0,1,2,3,4,4,5,6,7,8,8,9,10,11,12,12,13,14,15,16,16,17,18,19,20,21,22,
%T 23,24,24,25,26,27,28,28,29,30,31,32,32,33,34,35,36,36,37,38,39,40,41,
%U 42,43,44,44,45,46,47,48,48,49,50,51,52,52,53,54,55,56,56,57,58,59,60,61,62,63,64,64,65,66
%N a(0) = 0; a(n) = n - a(floor(a(n-1)/4)).
%C A variation on Hofstadter's G-sequence.
%H <a href="/index/Ho#Hofstadter">Index entries for Hofstadter-type sequences</a>
%F Conjecture: a(n) ~ c*n, where c = 1/(1 + 1/(4 + 1/(1 + 1/(4 + ...)))) = 2*(sqrt(2) - 1) = 0.82842712474619...
%t a[0] = 0; a[n_] := a[n] = n - a[Floor[a[n - 1]/4]]; Array[a, 80, 0]
%Y Cf. A005206, A286389, A366860, A366871.
%K nonn
%O 0,3
%A _Ilya Gutkovskiy_, Oct 26 2023
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