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A049816 Triangular array T read by rows: T(n,k)=number of nonzero remainders when Euclidean algorithm acts on n and k, for k=1,2,...,n, n=1,2,... 13

%I

%S 0,0,0,0,1,0,0,0,1,0,0,1,2,1,0,0,0,0,1,1,0,0,1,1,2,2,1,0,0,0,2,0,3,1,

%T 1,0,0,1,0,1,2,1,2,1,0,0,0,1,1,0,2,2,1,1,0,0,1,2,2,1,2,3,3,2,1,0,0,0,

%U 0,0,2,0,3,1,1,1,1,0,0,1,1,1,3,1,2,4,2,2,2,1,0

%N Triangular array T read by rows: T(n,k)=number of nonzero remainders when Euclidean algorithm acts on n and k, for k=1,2,...,n, n=1,2,...

%e Triangle begins:

%e 0,

%e 0, 0,

%e 0, 1, 0,

%e 0, 0, 1, 0,

%e 0, 1, 2, 1, 0,

%e 0, 0, 0, 1, 1, 0,

%e 0, 1, 1, 2, 2, 1, 0,

%e 0, 0, 2, 0, 3, 1, 1, 0,

%e 0, 1, 0, 1, 2, 1, 2, 1, 0,

%e 0, 0, 1, 1, 0, 2, 2, 1, 1, 0,

%e 0, 1, 2, 2, 1, 2, 3, 3, 2, 1, 0,

%e 0, 0, 0, 0, 2, 0, 3, 1, 1, 1, 1, 0,

%e 0, 1, 1, 1, 3, 1, 2, 4, 2, 2, 2, 1, 0,

%e ...

%t R[n_, k_] := R[n, k] = With[{r = Mod[n, k]}, If[r == 0, 1, R[k, r] + 1]];

%t T[n_, k_] := R[n, k] - 1;

%t Table[T[n, k], {n, 1, 13}, {k, 1, n}] // Flatten (* _Jean-Fran├žois Alcover_, Apr 12 2019, after _Robert Israel_ in A107435 *)

%K nonn,tabl

%O 1,13

%A _Clark Kimberling_

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Last modified July 27 11:29 EDT 2021. Contains 346304 sequences. (Running on oeis4.)