A332937 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give

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

(list; graph; refs; listen; history; text; internal format)

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