A317627 a(n) = A317253 - floor(8*n/3).

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, -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, 1, -1, 2, 1, -1, 1, 1, -1, 2, 3, 1, 1, 3, 1, 2

Offset: 1

Author

A.H.M. Smeets, Aug 02 2018

Keywords

• sign

Crossrefs

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

Programs

Python

n,f,i,p,q,base = 1,1,0,0,1,3
while i < 100000:
    i,p,q = i+1,p*base,q*base
    if i == f:
        p,n = p+1,n+1
        f = f*n
n,a,j = 0,0,0
while p%q > 0:
    a,f,p,q = a+1,p//q,q,p%q
    if f == 1:
        n = n+1
        print(n,a-1-(8*n//3))

Formula

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.

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

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

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

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