A106740 - OEIS

A106740

Triangle read by rows: greatest common divisors of pairs of Fibonacci numbers greater than 1: T(n, k) = gcd(Fibonacci(n), Fibonacci(k)).

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

3,1

LINKS

G. C. Greubel, Rows n = 3..52 of the triangle, flattened

FORMULA

T(n, k) = gcd(A000045(n), A000045(k)) for n >= 3 and 3 <= k <= n.

T(n, 3) = abs(A061347(n)).

T(n, 4) = A093148(n-1).

T(n, n) = A000045(n).

From G. C. Greubel, Sep 11 2021: (Start)

T(n, 3) = A131534(n-2).

T(n, 5) = A060904(n).

T(n, 6) = A010125(n).

T(n, n-1) = T(n, n-2) = A000012(n).

T(n, n-3) = A093148(n-5).

T(n, n-4) = A093148(n-5).

T(n, n-5) = A060904(n-5).

T(n, n-6) = A010125(n-6). (End)

EXAMPLE

Triangle begins as:

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;

MATHEMATICA

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 *)

PROG

(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

CROSSREFS

Cf. A000012, A000045, A010125, A060904, A061347, A093148, A131534.

Sequence in context: A026807 A338440 A179045 * A178534 A110619 A354234

Adjacent sequences: A106737 A106738 A106739 * A106741 A106742 A106743

KEYWORD

nonn,tabl

AUTHOR

Reinhard Zumkeller, May 15 2005

STATUS

approved