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a(n) = b(b(n+1)) - b(n-b(n)+1) where b(n) = A004001(n).
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%I #16 Mar 14 2017 00:26:54

%S 0,0,0,0,0,0,0,0,1,1,1,0,0,0,0,0,1,2,2,2,2,2,2,1,1,1,0,0,0,0,0,0,1,2,

%T 3,3,3,3,4,4,4,4,4,4,3,3,3,3,3,3,2,2,2,1,1,1,1,0,0,0,0,0,0,0,1,2,3,4,

%U 4,4,4,5,6,6,6,6,7,7,7,7,7,7,6,6,6,6,7,7,7,7,7

%N a(n) = b(b(n+1)) - b(n-b(n)+1) where b(n) = A004001(n).

%H Altug Alkan, <a href="/A283655/b283655.txt">Table of n, a(n) for n = 1..10000</a>

%H Altug Alkan, <a href="/A283655/a283655.png">Illustration of A283655</a>

%e a(1) = 0 since a(1) = A004001(A004001(2)) - A004001(1-A004001(1)+1) = 1 - 1 = 0.

%t b[1] = 1; b[2] = 1; b[n_] := b[n] = b[b[n - 1]] + b[n - b[n - 1]]; a[n_] := b[b[n + 1]] - b[n - b[n] + 1]; Array[a, 100] (* _Robert G. Wilson v_, Mar 13 2017 *)

%o (PARI) a=vector(1001); a[1]=a[2]=1; for(n=3, #a, a[n]=a[a[n-1]]+a[n-a[n-1]]); va = vector(1000, n, a[a[n+1]]-a[n+1-a[n]])

%Y Cf. A004001, A004074, A233270, A249071.

%K nonn

%O 1,18

%A _Altug Alkan_, Mar 13 2017