A330827 - OEIS

%I #27 Jan 14 2020 00:54:07

%S 1,1,1,1,1,1,3,1,1,1,1,3,1,3,1,5,3,3,5,3,5,3,3,1,3,1,1,1,1,3,1,3,3,5,

%T 3,5,3,5,5,5,7,5,7,7,5,9,7,7,11,7,9,7,7,7,11,9,13,5,9,5,15,7,9,7,7,7,

%U 7,7,5,5,5,3,5,3,5,3,3,1,3,1,1,1,1,3,1,3

%N a(n) is the numbers of ways to write 2*n = u + v where the ternary representations of u and of v have the same number of digits d for d = 0..2.

%C In other words, a(n) is the number of ways to write 2*n as the sum of two ternary anagrams.

%C Leading zeros are ignored.

%C Two ternary anagrams have necessarily the same parity, hence an odd number cannot be the sum of two ternary anagrams.

%H Rémy Sigrist, <a href="/A330827/b330827.txt">Table of n, a(n) for n = 0..19683</a>

%H Rémy Sigrist, <a href="/A330827/a330827.gp.txt">PARI program for A330827</a>

%H Rémy Sigrist, <a href="/A330827/a330827.png">Scatterplot of (x, y) such that 0 <= x, y <= 3^7 and x and y are ternary anagrams</a> (a(n) corresponds to the number of pixels (x, y) such that x+y = n)

%e For n = 6:

%e - we can write 12 as u + v in the following ways:

%e   u  v  ter(u)  ter(v)

%e   -  -  ------  ------

%e   5  7      12      21

%e   6  6      20      20

%e   7  5      21      12

%e - hence a(6) = 3.

%o (PARI) See Links section.

%Y Cf. A331216 (binary analog), A331218 (decimal analog).

%K nonn,base

%O 0,7

%A _Rémy Sigrist_, Jan 12 2020