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

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A347735 Square array T(n, k), n, k > 0, read by antidiagonals; let b be the function that associates to any pair of integers (u, v) the Bézout coefficients (x, y) as produced by the extended Euclidean algorithm (u*x + v*y = gcd(u, v)); T(n, k) is the number of iterations of b when starting from (n, k) needed to obtain a unit vector. 1
1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 2, 2, 1, 2, 1, 1, 1, 2, 2, 1, 2, 2, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 3, 1, 3, 1, 1, 1, 1, 1, 2, 2, 2, 3, 2, 2, 3, 2, 2, 2, 1, 1, 1, 2, 2, 2, 2, 1, 2, 2, 2, 2, 1, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,8

COMMENTS

For n, k > 0, b(n, k) = (A345415(n, k), A345416(n, k)).

LINKS

Table of n, a(n) for n=1..91.

Rémy Sigrist, Colored representation of the array for n, k <= 1000

Wikipedia, Bézout's identity

FORMULA

T(n, k) = T(k, n).

T(n, n) = 1.

T(m*n, m*k) = T(n, k) for any m > 0.

EXAMPLE

Array T(n, k) begins:

n\k| 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

---+---------------------------------------------------

1| 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

2| 1 1 2 1 2 1 2 1 2 1 2 1 2 1 2

3| 1 2 1 2 2 1 2 2 1 2 2 1 2 2 1

4| 1 1 2 1 2 2 2 1 2 2 2 1 2 2 2

5| 1 2 2 2 1 2 3 3 2 1 2 3 3 2 1

6| 1 1 1 2 2 1 2 2 2 2 2 1 2 2 2

7| 1 2 2 2 3 2 1 2 3 3 3 3 2 1 2

8| 1 1 2 1 3 2 2 1 2 2 3 2 3 2 2

9| 1 2 1 2 2 2 3 2 1 2 3 2 3 3 2

10| 1 1 2 2 1 2 3 2 2 1 2 2 3 3 2

PROG

(PARI) T(n, k) = { for (v=0, oo, if (n^2+k^2<=1, return (v), [n, k]=gcdext(n, k)[1..2])) }

CROSSREFS

Cf. A003989, A345415, A345416.

Sequence in context: A274013 A172086 A339047 * A204014 A339184 A156839

Adjacent sequences: A347732 A347733 A347734 * A347736 A347737 A347738

KEYWORD

nonn,tabl

AUTHOR

Rémy Sigrist, Sep 11 2021

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified February 7 06:02 EST 2023. Contains 360112 sequences. (Running on oeis4.)