|
|
A198069
|
|
Table read by rows, T(0,0) = 1 and for n>0, 0<=k<=2^(n-1) T(n,k) = gcd(k,2^(n-1)).
|
|
5
|
|
|
1, 1, 1, 2, 1, 2, 4, 1, 2, 1, 4, 8, 1, 2, 1, 4, 1, 2, 1, 8, 16, 1, 2, 1, 4, 1, 2, 1, 8, 1, 2, 1, 4, 1, 2, 1, 16, 32, 1, 2, 1, 4, 1, 2, 1, 8, 1, 2, 1, 4, 1, 2, 1, 16, 1, 2, 1, 4, 1, 2, 1, 8, 1, 2, 1, 4, 1, 2, 1, 32, 64, 1, 2, 1, 4, 1, 2, 1, 8, 1, 2, 1, 4, 1, 2
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,4
|
|
LINKS
|
|
|
FORMULA
|
For n > 0: Let S be the n-th row, S' = replace the initial term by its double, then row (n+1) = concatenation of S' and the reverse of S' without the initial term. - Reinhard Zumkeller, May 26 2013
|
|
EXAMPLE
|
1
1, 1
2, 1, 2
4, 1, 2, 1, 4
8, 1, 2, 1, 4, 1, 2, 1, 8
16, 1, 2, 1, 4, 1, 2, 1, 8, 1, 2, 1, 4, 1, 2, 1, 16
|
|
MAPLE
|
# In triangular form:
seq(print(seq(gcd(k, 2^(n-1)), k=0..2^(n-1))), n=0..6);
|
|
MATHEMATICA
|
Join[{1}, Flatten[Table[GCD[k, 2^(n-1)], {n, 10}, {k, 0, 2^(n-1)}]]] (* Harvey P. Dale, Oct 30 2021 *)
|
|
PROG
|
(Haskell)
a198069 n k = a198069_tabf !! n !! k
a198069_row n = a198069_tabf !! n
a198069_tabf = [0] : iterate f [1, 1] where
f (x:xs) = ys ++ tail (reverse ys) where ys = (2 * x) : xs
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,tabf
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|