%I #15 Mar 31 2024 08:48:15

%S 0,1,3,3,2,5,2,7,1,4,3,3,4,5,5,5,5,5,6,7,7,8,6,5,7,9,6,8,9,8,7,10,8,

%T 11,7,10,9,10,12,10,9,10,9,8,12,12,9,15,11,14,10,11,10,8,12,10,12,14,

%U 14,12,13,13,15,14,12,8,15,13,12,16,14,15,15,16,17,17,14,14,14,10,15,18,14,18

%N a(n) = 1 + a(n - a(n-1)) (n - a(n-1)) mod 2 + (n - a(n-2)) mod 3, with a(0) = 0, a(1) = 1.

%H G. C. Greubel, <a href="/A110897/b110897.txt">Table of n, a(n) for n = 0..10000</a>

%t a[n_]:= a[n]= If[n<2, n, 1 +a[n-a[n-1]] +Mod[n-a[n-2],3] -Mod[n-a[n-1],2]];

%t Table[a[n], {n,0,100}]

%o (Magma) [n le 2 select n-1 else 1 + Self(n-Self(n-1)) - ((n+1-Self(n-1)) mod 2) + ((n+2-Self(n-2)) mod 3) : n in [1..101]]; // _G. C. Greubel_, Mar 30 2024

%o (SageMath)

%o @CachedFunction

%o def a(n): # a = A110897

%o if n<2: return n

%o else: return 1 +a(n-a(n-1)) -(n-a(n-1))%2 +(n-a(n-2))%3

%o [a(n) for n in range(101)] # _G. C. Greubel_, Mar 30 2024

%Y Cf. A110898, A206012.

%K nonn,easy,less

%O 0,3

%A _Roger L. Bagula_, Sep 20 2005

%E Edited by _G. C. Greubel_, Mar 30 2024