A267179 Irregular triangle read by rows: successive bottom and right-hand borders of the infinite square array in A072030 (number of subtraction steps needed to compute GCD) read mod 2.

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

Offset

1

Links

R. J. Mathar, Table of n, a(n) for n = 1..10000

Example

The array in A072030 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 successive bottom and right-hand borders read mod 2 are:
1,
0, 1, 0,
1, 1, 1, 1, 1,
0, 0, 0, 1, 0, 0, 0,
1, 0, 0, 1, 1, 1, 0, 0, 1,
0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0,
1, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1,
0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0,
...

Maple

A267179 := proc(n, k)
        A267177(n, k) mod 2 ;
end proc:
seq(seq(A267179(n, k), k=1..2*n-1), n=1..10) ; # R. J. Mathar, May 08 2016

Mathematica

A072030[n_, k_] := A072030[n, k] = Which[n < 1 || k < 1, 0, n == k, 1, n < k, A072030[k, n], True, 1+A072030[k, n-k]];
A267179[n_, k_] := If[k <= n, A072030[n, k], A072030[2n-k, n]]~Mod~2;
Table[A267179[n, k], {n, 1, 10}, {k, 1, 2n-1}] // Flatten (* Jean-François Alcover, Apr 23 2023, after R. J. Mathar *)

Prog

(PARI)
tabl(nn) = {for (n=1, nn,
for (k=1, n, a = n; b = k; r = 1; s = 0; while (r, q = a\b; r = a - b*q; s += q; a = b; b = r); print1(s%2, ", "); );
for (k=1, n-1, a = n; b = n-k; r = 1; s = 0; while (r, q = a\b; r = a - b*q; s += q; a = b; b = r); print1(s%2, ", "); );
print(); ); }
tabl(12)

Crossrefs

This is A267177 read mod 2.

Cf. A072030.

Sequence in context: A267442 A267129 A267848 * A244527 A243566 A266112

Adjacent sequences: A267176 A267177 A267178 * A267180 A267181 A267182

Keyword

nonn,tabf

Author

N. J. A. Sloane, Jan 14 2016

Status

approved