OFFSET
0,2
COMMENTS
Table shows differences of a given power of 3 to the powers of 2 (columns), and differences of the powers of 3 to a given power of 2 (rows), respectively.
Note that positive terms (table's upper right area) and negative terms (lower left area) are separated by an imaginary line with slope -log(3)/log(2) = -1.5849625.. (see A020857). This "border zone" of the table is of interest in terms of how close powers of 3 and powers of 2 can get: i.e., those T(n,k) where k/n is a good rational approximation to log(3)/log(2), see A254351 for numerators k and respective A060528 for denominators n.
LINKS
K. G. Stier, Table of n, a(n) for n = 0..5150
EXAMPLE
Table begins
0 2 8 26 80..
-1 1 7 25 79..
-3 -1 5 23 73..
-7 -5 1 19 65..
-15 -13 -7 11 49..
.. .. .. .. ..
MATHEMATICA
Table[3^(n-k) - 2^k, {n, 0, 10}, {k, 0, n}] // Flatten (* Jean-François Alcover, Dec 18 2017 *)
PROG
(PARI) for(i=0, 10, {
for(j=0, i, print1((3^(i-j)-2^j), ", "))
});
CROSSREFS
Row 0 (=3^n-1) is A024023.
Row 1 (=3^n-2) is A058481.
Row 2 (=3^n-4) is A168611.
Column 0 (=1-2^n) is (-1)A000225.
Column 1 (=3-2^n) is (-1)A036563.
Column 2 (=9-2^n) is (-1)A185346.
Column 3 (=27-2^n) is (-1)A220087.
0,0-Diagonal (=3^n-2^n) is A001047.
0,1-Diagonal (=3^n-2^(n+1)) is A003063.
0,2-Diagonal (=3^n-2^(n+2)) is A214091.
KEYWORD
sign,tabl
AUTHOR
K. G. Stier, Jan 22 2015
STATUS
approved