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 A049828 Triangular array T given by rows: T(n,k)=sum of remainders when Euclidean algorithm acts on n,k; for k=1,2,...,n; n >= 1. 8
 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 3, 1, 0, 0, 0, 0, 2, 1, 0, 0, 1, 1, 4, 3, 1, 0, 0, 0, 3, 0, 6, 2, 1, 0, 0, 1, 0, 1, 5, 3, 3, 1, 0, 0, 0, 1, 2, 0, 6, 4, 2, 1, 0, 0, 1, 3, 4, 1, 6, 8, 6, 3, 1, 0, 0, 0, 0, 0, 3, 0, 8, 4, 3, 2, 1, 0, 0, 1, 1, 1, 6, 1, 7, 11, 5, 4, 3, 1, 0 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,13 COMMENTS For a fixed n, {(k,T(n,k)), k=1..n} is conjectured to be fractal in nature (see link). - Tiberiu Szocs-Mihai, Aug 17 2015 LINKS Robert Israel, Table of n, a(n) for n = 1..10011 (rows 1 to 141, flattened) Tiberiu Szocs-Mihai, Euclidean fractal (conjectured), Math Ticks Blog, January 2011. Tiberiu Szocs-Mihai, Euclidean fractal candidate description, Math Ticks Blog, January 2011. Eric Weisstein's World of Mathematics, Euclidean Algorithm. EXAMPLE Rows: 0; 0, 0; 0, 1, 0; 0, 0, 1, 0; 0, 1, 3, 1, 0; 0, 0, 0, 2, 1, 0; 0, 1, 1, 4, 3, 1, 0; ... MAPLE T:=  proc(n, k) option remember; if n*k = 0 then 0 else (n mod k) + procname(k, n mod k) fi end proc: seq(seq(T(n, k), k=1..n), n=1..20); # Robert Israel, Aug 31 2015 MATHEMATICA T[n_, k_] := T[n, k] = If[n*k == 0, 0, Mod[n, k] + T[k, Mod[n, k]]]; Table[T[n, k], {n, 1, 20}, {k, 1, n}] // Flatten (* Jean-François Alcover, Feb 27 2019, after Robert Israel *) PROG (PARI) tabl(nn) = {for (n=1, nn, for (k=1, n, a = n; b = k; r = 1; s = 0; while (r, q = a\b; r = a - b*q; s +=r; a = b; b = r); print1(s, ", "); ); print(); ); } \\ Michel Marcus, Aug 17 2015 CROSSREFS Row sums are in A049829. Sequence in context: A243827 A059530 A193525 * A286131 A285631 A316836 Adjacent sequences:  A049825 A049826 A049827 * A049829 A049830 A049831 KEYWORD nonn,tabl AUTHOR STATUS approved

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Last modified April 13 02:47 EDT 2021. Contains 342934 sequences. (Running on oeis4.)