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

1,3

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.

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

Links

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

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 (positions of 1's).

Sequence in context: A086198 A086196 A373063 * A350351 A138297 A374724

Adjacent sequences: A332934 A332935 A332936 * A332938 A332939 A332940

Keyword

nonn,easy

Author

Clark Kimberling, Mar 03 2020

Extensions

More terms from Antti Karttunen, Jan 15 2025

Status

approved