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%I #14 Aug 01 2018 03:12:31
%S 1,1,2,3,4,5,6,6,7,7,8,8,9,9,10,10,11,11,12,12,13,14,14,15,16,16,17,
%T 18,18,19,20,20,21,22,22,23,24,24,25,26,26,27,28,28,29,30,30,31,32,32,
%U 33,34,34,35,36,37,37,38,39,40,40,41,42,43,43,44,45,46,46,47,48,49,49,50,51,52
%N a(1) = a(2) = 1; for n >= 3, a(n) = a(t(n)) + a(n-t(n)) where t = A000195.
%C This sequence hits every positive integer.
%H Altug Alkan, <a href="/A317442/a317442_1.png">A log plot of a(n)/n</a>
%F a(n+1) - a(n) = 0 or 1 for all n >= 1.
%t Nest[Function[{a, n}, Append[a, a[[Floor@ Log@ n]] + a[[n - Floor@ Log@ n]] ] ] @@ {#, Length@ # + 1} &, {1, 1}, 74] (* _Michael De Vlieger_, Jul 30 2018 *)
%o (PARI) q=vector(100); for(n=1, 2, q[n]=1); for(n=3, #q, q[n]=q[floor(log(n))] + q[n-floor(log(n))]); q
%Y Cf. A000195, A316434.
%K nonn
%O 1,3
%A _Altug Alkan_, Jul 28 2018