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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. 4
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 (list; table; graph; refs; listen; history; text; internal format)
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

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

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Last modified December 4 04:49 EST 2021. Contains 349469 sequences. (Running on oeis4.)