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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
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 (list; table; graph; refs; listen; history; text; internal format)
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 * A085252 A250214 A073423

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

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Last modified February 24 04:30 EST 2020. Contains 332197 sequences. (Running on oeis4.)