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a(n) = A317253 - floor(8*n/3).
2

%I #8 Aug 13 2018 13:37:48

%S 2,3,1,1,3,1,2,1,-1,1,3,1,2,3,1,1,1,-1,2,1,-1,1,3,1,2,3,1,1,3,1,2,1,

%T -1,1,1,-1,2,3,1,1,1,-1,2,1,-1,1,3,1,2,3,1,1,3,1,2,1,-1,1,3,1,2,3,1,1,

%U 1,-1,2,1,-1,1,1,-1,2,3,1,1,3,1,2

%N a(n) = A317253 - floor(8*n/3).

%F a(3*n+1) = 2 - (n mod 2) for n >= 0, a(6*n+2) = 3 - 2*(n mod 2) and a(6*n+5) = a(3*n+2) for n >= 0, a(6*n+3) = 1 - 2*(n mod 2) and a(6*n+6) = a(3*n+3) for n >= 0.

%F a(3*n+1) = A000034(n+1) for n >= 0.

%F a(3*n+2) = A089607(n) for n > 1.

%F a(3*n+2) = 2*A014577(n-1)+1 for n > 0.

%F a(3*n+3) = A034947(n) = 2*A014577(n-1)-1 for n > 0.

%o (Python)

%o n,f,i,p,q,base = 1,1,0,0,1,3

%o while i < 100000:

%o ....i,p,q = i+1,p*base,q*base

%o ....if i == f:

%o ........p,n = p+1,n+1

%o ........f = f*n

%o n,a,j = 0,0,0

%o while p%q > 0:

%o ....a,f,p,q = a+1,p//q,q,p%q

%o ....if f == 1:

%o ........n = n+1

%o ........print(n,a-1-(8*n//3))

%Y Cf. A000034, A014577, A034947,A089607, A317414.

%K sign

%O 1,1

%A _A.H.M. Smeets_, Aug 02 2018