A267178 Array read by antidiagonals: T(n,k) = parity of number of steps in simple Euclidean algorithm for gcd(n,k) where n >= 1, k >= 1.

1, 0, 0, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0

Offset

1

Links

R. J. Mathar, Table of n, a(n) for n = 1..4950

Example

The array A072030 (before it is reduced mod 2) begins:
  1, 2, 3, 4, 5, 6, 7, 8, 9, 10, ...
  2, 1, 3, 2, 4, 3, 5, 4, 6, 5, ...
  3, 3, 1, 4, 4, 2, 5, 5, 3, 6, ...
  4, 2, 4, 1, 5, 3, 5, 2, 6, 4, ...
  5, 4, 4, 5, 1, 6, 5, 5, 6, 2, ...
  6, 3, 2, 3, 6, 1, 7, 4, 3, 4, ...
  7, 5, 5, 5, 5, 7, 1, 8, 6, 6, ...
  8, 4, 5, 2, 5, 4, 8, 1, 9, 5, ...
  9, 6, 3, 6, 6, 3, 6, 9, 1, 10, ...
  10, 5, 6, 4, 2, 4, 6, 5, 10, 1, ...
  ...
The first few antidiagonals read mod 2 are:
  1,
  0, 0,
  1, 1, 1,
  0, 1, 1, 0,
  1, 0, 1, 0, 1,
  0, 0, 0, 0, 0, 0,
  1, 1, 0, 1, 0, 1, 1,
  0, 1, 0, 1, 1, 0, 1, 0,
  1, 0, 1, 1, 1, 1, 1, 0, 1,
  0, 0, 1, 1, 0, 0, 1, 1, 0, 0,
  1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1,
  0, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 0,
  1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1,
  ...

Maple

A267178 := proc(n, k)
    A072030(n, k) mod 2 ;
end proc:
seq(seq(A267178(d-k, k), k=1..d-1), d=2..12) ; # R. J. Mathar, May 08 2016

Mathematica

T[n_, k_] := T[n, k] = Which[n < 1 || k < 1, 0, n == k, 1, n < k, T[k, n], True, 1+T[k, n-k]] // Mod[#, 2]&;
Table[T[d-k, k], {d, 2, 15}, {k, 1, d-1}] // Flatten (* Jean-François Alcover, Apr 25 2023 *)

Prog

(PARI)
tabl(nn) = {for (n=1, nn,
for (k=1, n, a = n-k+1; b = k; r = 1; s = 0; while (r, q = a\b; r = a - b*q; s += q; a = b; b = r); s2=s%2; print1(s2, ", "); );
print(); ); }
tabl(10)

Crossrefs

This is A072030 read mod 2.

Sequence in context: A267037 A200246 A267292 * A285277 A116937 A267810

Adjacent sequences: A267175 A267176 A267177 * A267179 A267180 A267181

Keyword

nonn,tabl

Author

N. J. A. Sloane, Jan 14 2016

Status

approved