A004493 Tersum n + 4.

4, 5, 3, 7, 8, 6, 1, 2, 0, 13, 14, 12, 16, 17, 15, 10, 11, 9, 22, 23, 21, 25, 26, 24, 19, 20, 18, 31, 32, 30, 34, 35, 33, 28, 29, 27, 40, 41, 39, 43, 44, 42, 37, 38, 36, 49, 50, 48, 52, 53, 51, 46, 47, 45, 58, 59, 57, 61

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

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

Crossrefs

Cf. A004489 (tersum array).

Programs

Mathematica

LinearRecurrence[{1, 0, 0, 0, 0, 0, 0, 0, 1, -1}, {4, 5, 3, 7, 8, 6, 1, 2, 0, 13, 14}, 80] (* Jinyuan Wang, Mar 10 2020 *)

PARI

my(table=[4,4,1,4,4,1,-5,-5,-8]); a(n) = n + table[n%9+1]; \\ Kevin Ryde, Apr 05 2021

Python

def tersum(a, b):
  c, pow3 = 0, 1
  while a + b > 0:
    a, ra = divmod(a, 3)
    b, rb = divmod(b, 3)
    c, pow3 = c + pow3*((ra+rb)%3), pow3*3
  return c
def a(n): return tersum(n, 4)
print([a(n) for n in range(58)]) # Michael S. Branicky, Apr 05 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.