The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A343836 Array T(n, k), n, k > 0, read by antidiagonals; the balanced ternary representation of T(n, k) is obtained by adding componentwise (i.e., without carries) the digits in the balanced ternary representations of n and of k. 1
 0, 1, 1, 2, -1, 2, 3, 3, 3, 3, 4, 4, -2, 4, 4, 5, 2, -4, -4, 2, 5, 6, 6, -3, -3, -3, 6, 6, 7, 7, 10, -2, -2, 10, 7, 7, 8, 5, 8, 8, -4, 8, 8, 5, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 13, 10, 10, -5, 10, 10, 13, 10, 10, 11, 8, 11, 11, 8, -7, -7, 8, 11, 11, 8, 11 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS This sequence is similar to A003987 and to A004489. We use the following table to combine individual digits (this is the balanced ternary addition table read mod 3): | T 0 1 ---+------- T | 1 T 0 0 | T 0 1 1 | 0 1 T LINKS Rémy Sigrist, Table of n, a(n) for n = 0..10010 Rémy Sigrist, Colored representation of the table for n, k < 1094 (blue denotes negative values, red denotes positive values, dark colors correspond to small values in absolute value) Wikipedia, Balanced ternary: Addition, subtraction and multiplication and division FORMULA T(n, k) = T(k, n). T(m, T(n, k)) = T(T(m, n), k). T(n, 0) = n. T(n, n) = -n. EXAMPLE Array T(n, k) begins: n\k| 0 1 2 3 4 5 6 7 8 9 10 11 12 13 ---+----------------------------------------------------------------- 0| 0 1 2 3 4 5 6 7 8 9 10 11 12 13 1| 1 -1 3 4 2 6 7 5 9 10 8 12 13 11 2| 2 3 -2 -4 -3 10 8 9 13 11 12 7 5 6 3| 3 4 -4 -3 -2 8 9 10 11 12 13 5 6 7 4| 4 2 -3 -2 -4 9 10 8 12 13 11 6 7 5 5| 5 6 10 8 9 -5 -7 -6 -11 -13 -12 -8 -10 -9 6| 6 7 8 9 10 -7 -6 -5 -13 -12 -11 -10 -9 -8 7| 7 5 9 10 8 -6 -5 -7 -12 -11 -13 -9 -8 -10 8| 8 9 13 11 12 -11 -13 -12 -8 -10 -9 -5 -7 -6 9| 9 10 11 12 13 -13 -12 -11 -10 -9 -8 -7 -6 -5 10| 10 8 12 13 11 -12 -11 -13 -9 -8 -10 -6 -5 -7 11| 11 12 7 5 6 -8 -10 -9 -5 -7 -6 -11 -13 -12 12| 12 13 5 6 7 -10 -9 -8 -7 -6 -5 -13 -12 -11 13| 13 11 6 7 5 -9 -8 -10 -6 -5 -7 -12 -11 -13 Array T(n, k) begins in balanced ternary: n\k| 0 1 1T 10 11 1TT 1T0 1T1 10T 100 101 11T 110 111 ---+---------------------------------------------------------------------- 0| 0 1 1T 10 11 1TT 1T0 1T1 10T 100 101 11T 110 111 1| 1 T 10 11 1T 1T0 1T1 1TT 100 101 10T 110 111 11T 1T| 1T 10 T1 TT T0 101 10T 100 111 11T 110 1T1 1TT 1T0 10| 10 11 TT T0 T1 10T 100 101 11T 110 111 1TT 1T0 1T1 11| 11 1T T0 T1 TT 100 101 10T 110 111 11T 1T0 1T1 1TT 1TT| 1TT 1T0 101 10T 100 T11 T1T T10 TT1 TTT TT0 T01 T0T T00 1T0| 1T0 1T1 10T 100 101 T1T T10 T11 TTT TT0 TT1 T0T T00 T01 1T1| 1T1 1TT 100 101 10T T10 T11 T1T TT0 TT1 TTT T00 T01 T0T 10T| 10T 100 111 11T 110 TT1 TTT TT0 T01 T0T T00 T11 T1T T10 100| 100 101 11T 110 111 TTT TT0 TT1 T0T T00 T01 T1T T10 T11 101| 101 10T 110 111 11T TT0 TT1 TTT T00 T01 T0T T10 T11 T1T 11T| 11T 110 1T1 1TT 1T0 T01 T0T T00 T11 T1T T10 TT1 TTT TT0 110| 110 111 1TT 1T0 1T1 T0T T00 T01 T1T T10 T11 TTT TT0 TT1 111| 111 11T 1T0 1T1 1TT T00 T01 T0T T10 T11 T1T TT0 TT1 TTT PROG (PARI) T(n, k, c=v->centerlift(Mod(v, 3))) = { if (n==0 && k==0, return (0), my (d=c(n), t=c(k)); c(d+t)+3*T((n-d)/3, (k-t)/3)) } CROSSREFS Cf. A003987, A004489, A343316. Sequence in context: A343040 A343044 A003986 * A123603 A228506 A228285 Adjacent sequences: A343833 A343834 A343835 * A343837 A343838 A343839 KEYWORD sign,tabl,base AUTHOR Rémy Sigrist, May 01 2021 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified June 13 22:21 EDT 2024. Contains 373391 sequences. (Running on oeis4.)