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

1,1

Links

Table of n, a(n) for n=1..79.

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.

Prog

(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))

Crossrefs

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

Sequence in context: A300521 A385507 A356152 * A271566 A296659 A270823

Adjacent sequences: A317624 A317625 A317626 * A317628 A317629 A317630

Keyword

sign

Author

A.H.M. Smeets, Aug 02 2018

Status

approved