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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

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

Sequence in context: A243827 A059530 A193525 * A286131 A285631 A316836

Adjacent sequences:  A049825 A049826 A049827 * A049829 A049830 A049831

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling

STATUS

approved

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Last modified January 18 13:01 EST 2019. Contains 319271 sequences. (Running on oeis4.)