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A317206
An alternative tribonacci representation of n: an encoding of the position of n in the A003144, A003145, A003146 table.
4
0, 1, 2, 12, 3, 112, 22, 13, 1112, 212, 122, 32, 113, 23, 11112, 2112, 1212, 312, 1122, 222, 132, 1113, 213, 123, 33, 111112, 21112, 12112, 3112, 11212, 2212, 1312, 11122, 2122, 1222, 322, 1132, 232, 11113, 2113, 1213, 313, 1123, 223, 133, 1111112, 211112
OFFSET
0,3
COMMENTS
Let T denote the following 4-rowed table, whose rows are n, A = A003144(n), B = A003145(n), C = A003146(n):
n: 1 .2 .3 .4 .5 .6 .7 .8 .9 ...
A: 1 .3 .5 .7 .8 10 ...
B: 2 .6 .9 13 15 19 ...
C: 4 11 17 24 28 35 ...
Set a(0)=0. For n>0, locate n in rows A, B, C of the table, and indicate how to reach that entry starting from column 1. For example, 17 = C(3) = C(A(2)) = C(A(B(1))), so the path to reach 17 is CAB, which we write (encoding A as 1, B as 2, C as 3) as a(17) = 312.
This is an analog of the Wythoff representation of n described in Lang (1996), A189921, and A317208.
REFERENCES
W. Lang, The Wythoff and the Zeckendorf representations of numbers are equivalent, in G. E. Bergum et al. (edts.) Application of Fibonacci numbers vol. 6, Kluwer, Dordrecht, 1996, pp. 319-337. [See A317208 for a link.]
LINKS
Wolfdieter Lang, The Tribonacci and ABC Representations of Numbers are Equivalent, arXiv preprint arXiv:1810.09787 [math.NT], 2018.
CROSSREFS
See A278038 for the standard tribonacci representation of n.
See A189921 and A317208 for the analogous Wythoff representation of n.
Cf. A317207.
Sequence in context: A275841 A224841 A363932 * A164869 A347408 A248030
KEYWORD
nonn,base
AUTHOR
N. J. A. Sloane, Aug 09 2018
EXTENSIONS
Inserted a(10) and a(18) and beyond from Lars Blomberg, Aug 11 2018
STATUS
approved