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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 September 27 08:39 EDT 2021. Contains 347689 sequences. (Running on oeis4.)