A206567 S(m,n) = (number of nonzero terms common to the base 3 expansions of m and n), a symmetric matrix read by antidiagonals.

1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 2, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 2, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 1

Offset

1,25

Comments

Every nonnegative integer occurs infinitely many times in the matrix.

Links

Robert Israel, Table of n, a(n) for n = 1..10011 (antidiagonals 1 to 141, flattened)

Formula

Diagonal entries S(n,n) = A160384(n) since all nonzero digits match. - Robert Israel, Mar 18 2018

Example

Northwest corner:
1 0 0 1 0 0 1 0 0 1 0 0 1
0 1 0 0 1 0 0 1 0 0 1 0 0
0 0 1 1 1 0 0 0 0 0 0 1 1
1 0 1 2 1 0 1 0 0 1 0 1 2
0 1 1 1 2 0 0 1 0 0 1 1 1
0 0 0 0 0 1 1 1 0 0 0 0 0
1 0 0 1 0 1 2 1 0 1 0 0 1
0 1 0 0 1 1 1 2 0 0 1 0 0
0 0 0 0 0 0 0 0 1 1 1 1 1
1 0 0 1 0 0 1 0 1 2 1 1 2
0 1 0 0 1 0 0 1 1 1 2 1 1
0 0 1 1 1 0 0 0 1 1 1 2 2
1 0 1 2 1 0 1 0 1 2 1 2 3
4 = 3 + 1 and 13 = 3^2 + 3 + 1, so S(13,4)=2.

Maple

S:= proc(m, n) local M, N;
  M:= convert(m, base, 3);
  N:= convert(n, base, 3);
  convert(zip((s, t) -> `if`(s=t and s <> 0, 1, 0), M, N), `+`);
end proc:
seq(seq(S(k, n-k+1), k=1..n), n=1..30); # Robert Israel, Mar 19 2018

Mathematica

d[n_] := IntegerDigits[n, 3];
t[n_] := Reverse[Array[d, 100][[n]]]
s[n_, k_] := Position[t[n], k]
t[m_, n_] := Sum[Length[Intersection[s[m, k], s[n, k]]], {k, 1, 2}]
TableForm[Table[t[m, n], {m, 1, 24},
  {n, 1, 24}]]  (* A206567 as a matrix *)
Flatten[Table[t[i, n + 1 - i], {n, 1, 24},
  {i, 1, n}]]   (* A206567 as a sequence *)

Prog

(PARI) d(n) = Vecrev(digits(n, 3));
T(n, k) = {my(dn = d(n), dk = d(k), nb = min(#dn, #dk)); sum(i=1, nb, dn[i] && (dn[i] == dk[i])); } \\ Michel Marcus, Mar 19 2018

Crossrefs

Cf. A160384, A206479 (similar in base 2).

Sequence in context: A060154 A061007 A060838 * A362422 A085252 A250214

Adjacent sequences: A206564 A206565 A206566 * A206568 A206569 A206570

Keyword

nonn,tabl,base

Author

Clark Kimberling, Feb 09 2012

Extensions

Edited by Robert Israel, Mar 19 2018

Status

approved