A004489 Table of tersums m + n (answers written in base 10).

0, 1, 1, 2, 2, 2, 3, 0, 0, 3, 4, 4, 1, 4, 4, 5, 5, 5, 5, 5, 5, 6, 3, 3, 6, 3, 3, 6, 7, 7, 4, 7, 7, 4, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 6, 6, 0, 6, 6, 0, 6, 6, 9, 10, 10, 7, 1, 1, 7, 1, 1, 7, 10, 10, 11, 11, 11, 2, 2, 2, 2, 2, 2, 11, 11, 11, 12, 9, 9, 12, 0, 0, 3, 0, 0, 12, 9, 9, 12, 13, 13, 10, 13, 13, 1, 4, 4, 1, 13, 13, 10, 13, 13

Offset

0,4

Links

Alois P. Heinz, Antidiagonals d = 0..140, flattened

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.

Example

Table begins:
  0 1 2 3 4 5 6 ...
  1 2 0 4 5 3 7 ...
  2 0 1 5 3 4 8 ...
  3 4 5 6 7 8 0 ...
  4 5 3 7 8 6 1 ...
  5 3 4 8 6 7 2 ...
  6 7 8 0 1 2 3 ...
  ...

Maple

T:= proc(n, m) local t, h, r, i;
      t, h, r:= n, m, 0;
      for i from 0 while t>0 or h>0 do
        r:= r +3^i *irem(irem(t, 3, 't') +irem(h, 3, 'h'), 3)
      od; r
    end:
seq(seq(T(n, d-n), n=0..d), d=0..12);  # Alois P. Heinz, Sep 07 2011

Mathematica

T[n_, m_] := Module[{t, h, r, i, remt, remh}, {t, h, r} = {n, m, 0}; For[i = 0, t>0 || h>0, i++, r = r + 3^i*Mod[({t, remt} = QuotientRemainder[t, 3 ]; remt) + ({h, remh} = QuotientRemainder[h, 3]; remh), 3]]; r]; Table[Table[T[n, d-n], {n, 0, d}], {d, 0, 13}] // Flatten (* Jean-François Alcover, Jan 07 2014, translated from Maple *)

Prog

(PARI) T(n, m) = fromdigits(Vec(Pol(digits(n, 3)) + Pol(digits(m, 3)))%3, 3); \\ Kevin Ryde, Apr 06 2021
(Python)
def T(n, m):
  k, pow3 = 0, 1
  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([T(n, d-n) for d in range(14) for n in range(d+1)]) # Michael S. Branicky, May 04 2021

Crossrefs

Similar to but different from A004481.

Main diagonal gives A004488.

Cf. A003987 (analogous sequence for base 2).

Sequence in context: A305383 A004481 A307296 * A305384 A112599 A347905

Adjacent sequences: A004486 A004487 A004488 * A004490 A004491 A004492

Keyword

nonn,base,tabl,look,easy,nice

Author

N. J. A. Sloane

Extensions

More terms from Larry Reeves (larryr(AT)acm.org), Jan 23 2001

Status

approved