A332937 a(n) is the greatest common divisor of the first two terms of row n of the Wythoff array (A035513).

1, 1, 2, 3, 4, 1, 1, 1, 2, 1, 1, 1, 3, 1, 2, 5, 1, 1, 6, 1, 1, 7, 1, 1, 8, 1, 1, 9, 2, 1, 10, 1, 1, 11, 2, 1, 1, 1, 1, 1, 2, 1, 3, 1, 4, 1, 2, 1, 1, 1, 2, 3, 1, 1, 2, 5, 4, 3, 1, 1, 2, 1, 1, 1, 1, 1, 6, 1, 1, 1, 2, 1, 2, 1, 1, 1, 4, 7, 1, 1, 1, 3, 2, 1, 1, 1

Offset

1,3

Comments

a(n) is also the gcd of every pair of consecutive terms of row n of the Wythoff array. Conjectures: the maximal number of consecutive 1's is 5, and the limiting proportion of 1's exists. See A332938.

Links

Table of n, a(n) for n=1..86.

Example

See A332938.

Mathematica

W[n_, k_] := Fibonacci[k + 1] Floor[n*GoldenRatio] + (n - 1) Fibonacci[k]; (* A035513 *)
t = Table[GCD[W[n, 1], W[n, 2]], {n, 1, 160}]  (* A332937 *)
Flatten[Position[t, 1]]  (* A332938 *)

Prog

(PARI) T(n, k) = (n+sqrtint(5*n^2))\2*fibonacci(k+1) + (n-1)*fibonacci(k); \\ A035513
a(n) = gcd(T(n, 0), T(n, 1)); \\ Michel Marcus, Mar 03 2020

Crossrefs

Cf. A000045, A173027, A173028, A035513, A332938.

Sequence in context: A339255 A086198 A086196 * A350351 A138297 A139458

Adjacent sequences: A332934 A332935 A332936 * A332938 A332939 A332940

Keyword

nonn,easy

Author

Clark Kimberling, Mar 03 2020

Status

approved