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%I #31 Jul 03 2018 02:40:13
%S 1,1,1,2,3,3,4,4,4,5,6,6,7,7,8,8,9,9,10,10,10,11,12,12,13,13,13,14,15,
%T 15,16,16,17,17,18,18,19,19,20,20,21,21,22,22,22,23,24,24,25,25,26,26,
%U 27,27,28,28,28,29,30,30,31,31,31,32,33,33,34,34,35,35,36,36,37,37,38,38
%N a(n) = a(phi(n)) + a(n-phi(n)) with a(1) = a(2) = a(3) = 1.
%C This sequence hits every positive integer and each term repeats at most three times.
%F a(n) = a(A000010(n)) + a(A051953(n)) with a(1) = a(2) = a(3) = 1.
%F a(n+1) - a(n) = 0 or 1 for all n >= 1.
%F lim_{n->infinity} a(n)/n = 1/2.
%t Nest[Append[#1, #1[[EulerPhi@ #2]] + #1[[#2 - EulerPhi@ #2]] ] & @@ {#, Length@ #} &, {1, 1, 1}, 88] (* _Michael De Vlieger_, Jul 01 2018 *)
%o (PARI) q=vector(99); for(n=1, 3, q[n] = 1); for(n=4, #q, q[n] = q[eulerphi(n)] + q[n-eulerphi(n)]); q
%o (GAP) a:=[1,1,1];; for n in [4..80] do a[n]:=a[Phi(n)]+a[n-Phi(n)]; od; a; # _Muniru A Asiru_, Jul 01 2018
%Y Cf. A000010, A051953.
%K nonn,easy
%O 1,4
%A _Altug Alkan_, Jul 01 2018
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