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A106740
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Triangle read by rows: greatest common divisors of pairs of Fibonacci numbers greater than 1: T(n, k) = gcd(Fibonacci(n), Fibonacci(k)).
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1
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2, 1, 3, 1, 1, 5, 2, 1, 1, 8, 1, 1, 1, 1, 13, 1, 3, 1, 1, 1, 21, 2, 1, 1, 2, 1, 1, 34, 1, 1, 5, 1, 1, 1, 1, 55, 1, 1, 1, 1, 1, 1, 1, 1, 89, 2, 3, 1, 8, 1, 3, 2, 1, 1, 144, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 233, 1, 1, 1, 1, 13, 1, 1, 1, 1, 1, 1, 377, 2, 1, 5, 2, 1, 1, 2, 5, 1, 2, 1, 1, 610
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OFFSET
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3,1
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LINKS
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FORMULA
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T(n, n-1) = T(n, n-2) = A000012(n).
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EXAMPLE
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Triangle begins as:
2;
1, 3;
1, 1, 5;
2, 1, 1, 8;
1, 1, 1, 1, 13;
1, 3, 1, 1, 1, 21;
2, 1, 1, 2, 1, 1, 34;
1, 1, 5, 1, 1, 1, 1, 55;
1, 1, 1, 1, 1, 1, 1, 1, 89;
2, 3, 1, 8, 1, 3, 2, 1, 1, 144;
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 233;
1, 1, 1, 1, 13, 1, 1, 1, 1, 1, 1, 377;
2, 1, 5, 2, 1, 1, 2, 5, 1, 2, 1, 1, 610;
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MATHEMATICA
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T[n_, k_]:= GCD[Fibonacci[n], Fibonacci[k]];
Table[T[n, k], {n, 3, 18}, {k, 3, n}]//Flatten (* G. C. Greubel, Sep 11 2021 *)
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PROG
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(Sage)
def T(n, k): return gcd(fibonacci(n), fibonacci(k))
flatten([[T(n, k) for k in (3..n)] for n in (3..18)]) # G. C. Greubel, Sep 11 2021
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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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