A004500 Tersum n + 11.

11, 9, 10, 14, 12, 13, 17, 15, 16, 20, 18, 19, 23, 21, 22, 26, 24, 25, 2, 0, 1, 5, 3, 4, 8, 6, 7, 38, 36, 37, 41, 39, 40, 44, 42, 43, 47, 45, 46, 50, 48, 49, 53, 51, 52, 29, 27, 28, 32, 30, 31, 35, 33, 34, 65, 63, 64, 68, 66, 67, 71, 69, 70, 74, 72, 73, 77, 75

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• base
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (1,0,1,-1,0,0,0,0,-1,1,0,1,-1,0,0,0,0,-1,1,0,1,-1).

Crossrefs

Cf. A004489.

Programs

Python

def a(n):
    k, pow3, m = 0, 1, 11
    while n + m > 0:
        n, rn = divmod(n, 3)
        m, rm = divmod(m, 3)
        k, pow3 = k + pow3*((rn+rm)%3), pow3*3
    return k
print([a(n) for n in range(58)]) # Michael S. Branicky, Nov 09 2021

Formula

Tersum m + n: write m and n in base 3 and add mod 3 with no carries; e.g., 5 + 8 = "21" + "22" = "10" = 1.

a(n) = A004489(n, 11). - Michel Marcus, Nov 09 2021

G.f.: (20*x^21+x^20-2*x^19-16*x^18-7*x^12+x^11-2*x^10+11*x^9-7*x^3+x^2-2*x+11) / ((x^2+x+1)*(x^18+x^9+1)*(x-1)^2). - Alois P. Heinz, Nov 09 2021