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%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
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