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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
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
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
KEYWORD
nonn,tabf
AUTHOR
N. J. A. Sloane, Jan 14 2016
STATUS
approved