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
Examples
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 ... ...
Links
- Alois P. Heinz, Antidiagonals d = 0..140, flattened
Crossrefs
Programs
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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 *) -
PARI
T(n,m) = fromdigits(Vec(Pol(digits(n,3)) + Pol(digits(m,3)))%3, 3); \\ Kevin Ryde, Apr 06 2021
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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
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.
Extensions
More terms from Larry Reeves (larryr(AT)acm.org), Jan 23 2001