A051011 Numerator of average of number of steps in Euclidean algorithm for all gcd(m,n) with 0<=m

0, 1, 1, 1, 8, 7, 13, 7, 16, 17, 27, 5, 32, 31, 31, 17, 46, 41, 55, 11, 50, 5, 73, 9, 68, 73, 25, 18, 96, 71, 101, 45, 32, 105, 101, 23, 124, 119, 41, 11, 146, 113, 155, 3, 44, 151, 177, 23, 164, 161, 169, 41, 204, 167, 183, 83, 64, 201, 231, 44, 240, 223, 209, 109

Offset: 1

Author

Eric W. Weisstein

Keywords

• nonn
• frac

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..1000
• Eric Weisstein's World of Mathematics, Euclidean Algorithm.

Crossrefs

Cf. A034883, A051010, A051012 (denominators).

Programs

Haskell

import Data.Ratio ((%), numerator)
a051011 n = numerator $ (sum $ a051010_row n) % n
-- 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]]]; a[n_] := Numerator[Sum[t[m, n], {m, 0, n}]/n]; Array[a, 100] (* Amiram Eldar, Apr 22 2022 after Jean-François Alcover at A051010 *)