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A267178
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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.
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4
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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)
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OFFSET
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1
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LINKS
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EXAMPLE
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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,
...
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MAPLE
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end proc:
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MATHEMATICA
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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]&;
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PROG
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(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)
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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