A111957 Triangle read by rows: T(n,k) = gcd(Fibonacci(n), Lucas(k)), 1 <= k <= n.

1, 1, 1, 1, 1, 2, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 7, 1, 3, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 4, 1, 1, 18, 1, 1, 4, 3, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 29, 1, 1, 1, 1, 1, 1

Offset

1,6

Links

G. C. Greubel, Table of n, a(n) for the first 50 rows, flattened

Paulo Ribenboim, FFF (Favorite Fibonacci Flowers), Fib. Quart. 43 (No. 1, 2005), 3-14.

Formula

T(n, k) = Lucas(g), where g = gcd(n, k), if n/g is even; = 2 if n/g is odd and 3|g; = 1 otherwise.

Example

Triangle begins:
1,
1, 1,
1, 1, 2,
1, 3, 1, 1,
1, 1, 1, 1, 1,
1, 1, 4, 1, 1, 2,
1, 1, 1, 1, 1, 1, 1,
1, 3, 1, 7, 1, 3, 1, 1,
1, 1, 2, 1, 1, 2, 1, 1, 2,
1, 1, 1, 1, 11, 1, 1, 1, 1, 1,
=============================

Mathematica

Flatten[Table[GCD[Fibonacci[n], LucasL[k]], {n, 20}, {k, n}]] (* Alonso del Arte, Dec 19 2015 *)

Prog

(Magma) /* As triangle */ [[Gcd(Fibonacci(n), Lucas(k)): k in [1..n]]: n in [1.. 15]]; // Vincenzo Librandi, Dec 20 2015

Crossrefs

Cf. A000045, A000032, A111946, A111956.

Sequence in context: A144966 A320000 A119805 * A125168 A324725 A373361

Adjacent sequences: A111954 A111955 A111956 * A111958 A111959 A111960

Keyword

nonn,tabl

Author

N. J. A. Sloane, Nov 28 2005

Status

approved