A317206 An alternative tribonacci representation of n: an encoding of the position of n in the A003144, A003145, A003146 table.

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

Lars Blomberg, Table of n, a(n) for n = 0..10000

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

Adjacent sequences: A317203 A317204 A317205 * A317207 A317208 A317209

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