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 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

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Last modified September 12 04:22 EDT 2024. Contains 375842 sequences. (Running on oeis4.)