cp's OEIS Frontend

A358915 a(n) is the far-difference representation of n written in balanced ternary.

%I A358915 #15 Dec 06 2022 09:47:50
%S A358915 0,1,3,9,26,27,78,80,81,82,234,240,242,243,244,246,702,703,720,726,
%T A358915 728,729,730,732,738,2105,2106,2107,2109,2160,2161,2178,2184,2186,
%U A358915 2187,2188,2190,2196,2213,2214,6315,6317,6318,6319,6321,6327,6479,6480,6481,6483
%N A358915 a(n) is the far-difference representation of n written in balanced ternary.
%C A358915 A far-difference representation of an integer is the unique way to write that integer of the sum/difference of Fibonacci numbers such that any two terms in the sum with the same sign differ by at least an index of 4 and any two terms with different signs differ by an index of at least 3.
%C A358915 This sequence is also the list of numbers whose balanced ternary representation has the property that all signed-digits with the same sign differ by at least 4 positions and all signed-digits with different signs differ by at least 3 positions.
%H A358915 Hannah Alpert, <a href="https://www.emis.de/journals/INTEGERS/papers/j57/j57.pdf">Differences of Multiple Fibonacci Numbers</a>, Integers, 9 (2009), 745-749.
%e A358915 Let F_i be the i-th term of the 0-indexed Fibonacci sequence beginning 1, 2, 3, 5, 8, ... .
%e A358915 | n  | far-difference               | a(n)                  |
%e A358915 |----+------------+-----------------+-----------------+-----+
%e A358915 | 10 | 13 - 3     | F_5 - F_2       | 3^5 - 3^2       | 234 |
%e A358915 | 11 | 13 - 2     | F_5 - F_1       | 3^5 - 3^1       | 240 |
%e A358915 | 12 | 13 - 1     | F_5 - F_0       | 3^5 - 3^0       | 242 |
%e A358915 | 13 | 13         | F_5             | 3^5             | 243 |
%e A358915 | 14 | 13 + 1     | F_5 + F_0       | 3^5 + 3^0       | 244 |
%e A358915 | 15 | 13 + 2     | F_5 + F_1       | 3^5 + 3^1       | 246 |
%e A358915 | 16 | 21 - 5     | F_6 - F_3       | 3^6 - 3^3       | 702 |
%e A358915 | 17 | 21 - 5 + 1 | F_6 - F_3 + F_0 | 3^6 - 3^3 + 3^0 | 703 |
%e A358915 | 18 | 21 - 3     | F_6 - F_2       | 3^6 - 3^2       | 720 |
%e A358915 | 19 | 21 - 2     | F_6 - F_1       | 3^6 - 3^1       | 726 |
%e A358915 | 20 | 21 - 1     | F_6 - F_0       | 3^6 - 3^0       | 728 |
%Y A358915 Cf. A003714, A097083, A105446, A117966.
%K A358915 nonn,base
%O A358915 0,3
%A A358915 _Peter Kagey_, Dec 05 2022