A051012 Denominator of average of number of steps in Euclidean algorithm for all gcd(m,n) with 0 <= m < n.

1, 2, 1, 1, 5, 6, 7, 4, 9, 10, 11, 3, 13, 14, 15, 8, 17, 18, 19, 5, 21, 2, 23, 4, 25, 26, 9, 7, 29, 30, 31, 16, 11, 34, 35, 9, 37, 38, 13, 4, 41, 42, 43, 1, 15, 46, 47, 8, 49, 50, 51, 13, 53, 54, 55, 28, 19, 58, 59, 15, 61, 62, 63, 32, 65, 6, 67, 17, 69, 70, 71, 36, 73, 74, 75

Offset

1,2

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

Eric Weisstein's World of Mathematics, Euclidean Algorithm.

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_] := Denominator[Sum[t[m, n], {m, 0, n}]/n]; Array[a, 100] (* Amiram Eldar, Apr 22 2022 after Jean-François Alcover at A051010 *)

Prog

(Haskell)
import Data.Ratio ((%), denominator)
a051012 n = denominator $ (sum $ a051010_row n) % n
-- Reinhard Zumkeller, Jun 27 2013

Crossrefs

Cf. A034883, A051010, A051011 (numerators).

Sequence in context: A176093 A092437 A064814 * A064644 A306444 A090210

Adjacent sequences: A051009 A051010 A051011 * A051013 A051014 A051015

Keyword

nonn,frac

Author

Eric W. Weisstein

Status

approved