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

%I A051010 #22 Feb 16 2025 08:32:41
%S A051010 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,
%T A051010 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,
%U A051010 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
%N A051010 Triangle T(m,n) giving of number of steps in the Euclidean algorithm for gcd(m,n) with 0<=m<n.
%H A051010 T. D. Noe, <a href="/A051010/b051010.txt">Rows n=1..100 of triangle, flattened</a>
%H A051010 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/EuclideanAlgorithm.html">Euclidean Algorithm.</a>
%t A051010 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 *)
%o A051010 (Haskell)
%o A051010 a051010 n k = snd $ until ((== 0) . snd . fst)
%o A051010                     (\((x, y), i) -> ((y, mod x y), i + 1)) ((n, k), 0)
%o A051010 a051010_row n = map (a051010 n) [0..n-1]
%o A051010 a051010_tabl = map a051010_row [1..]
%o A051010 -- _Reinhard Zumkeller_, Jun 27 2013
%Y A051010 Cf. A034883, A051011, A051012.
%Y A051010 Cf. A049826.
%Y A051010 Cf. A130130 (central terms).
%K A051010 nonn,nice,tabl
%O A051010 1,6
%A A051010 _Eric W. Weisstein_