A051010 Triangle T(m,n) giving of number of steps in the Euclidean algorithm for gcd(m,n) with 0<=m

0, 0, 1, 0, 1, 2, 0, 1, 1, 2, 0, 1, 2, 3, 2, 0, 1, 1, 1, 2, 2, 0, 1, 2, 2, 3, 3, 2, 0, 1, 1, 3, 1, 4, 2, 2, 0, 1, 2, 1, 2, 3, 2, 3, 2, 0, 1, 1, 2, 2, 1, 3, 3, 2, 2, 0, 1, 2, 3, 3, 2, 3, 4, 4, 3, 2, 0, 1, 1, 1, 1, 3, 1, 4, 2, 2, 2, 2, 0, 1, 2, 2, 2, 4, 2, 3, 5, 3, 3, 3, 2, 0, 1, 1, 3, 2, 3, 2, 1, 3, 4, 3

Offset: 1

Author

Eric W. Weisstein

Keywords

• nonn
• nice
• tabl

Links

• T. D. Noe, Rows n=1..100 of triangle, flattened
• Eric Weisstein's World of Mathematics, Euclidean Algorithm.

Crossrefs

Cf. A034883, A051011, A051012.

Cf. A049826.

Cf. A130130 (central terms).

Programs

Haskell

a051010 n k = snd $ until ((== 0) . snd . fst)
                    (\((x, y), i) -> ((y, mod x y), i + 1)) ((n, k), 0)
a051010_row n = map (a051010 n) [0..n-1]
a051010_tabl = map a051010_row [1..]
-- Reinhard Zumkeller, Jun 27 2013

Mathematica

t[m_, n_] := For[r[-1]=m; r[0]=n; k=1, True, k++, r[k] = Mod[r[k-2], r[k-1]]; If[r[k] == 0, Return[k-1]]]; Table[ t[m, n] , {n, 1, 14}, {m, 0, n-1}] // Flatten (* Jean-François Alcover, Oct 25 2012 *)