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, 2, 1, 8, 1, 3, 1, 2, 1, 1, 5, 12, 1, 2, 1, 1, 1, 2, 1, 13, 3, 1, 1

Offset: 1

Author

Clark Kimberling, Mar 03 2020

Keywords

• nonn
• easy

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.

If seems that for all primes p > 3, a(1+p) = 1. - Antti Karttunen, Jan 15 2025

Examples

			See A332938.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000

Crossrefs

Cf. A000045, A173027, A173028, A035513, A332938 (positions of 1's).

Programs

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 *)

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

Extensions

More terms from Antti Karttunen, Jan 15 2025