A383346 Representation of n in rational base 3/2.

0, 2, 21, 210, 212, 2101, 2120, 2122, 21011, 21200, 21202, 21221, 210110, 210112, 212001, 212020, 212022, 212211, 2101100, 2101102, 2101121, 2120010, 2120012, 2120201, 2120220, 2120222, 2122111, 21011000, 21011002, 21011021, 21011210, 21011212, 21200101, 21200120

Offset

0,2

Comments

Differs from A024629 by that here a factor 1/b is pulled out of the sum (with base a/b).

Links

Table of n, a(n) for n=0..33.

Shalom Eliahou and Jean-Louis Verger-Gaugry, The number system in rational base 3/2 and the 3x+1 problem, arXiv:2504.13716 [math.NT], 2024. See Table 1 p. 3.

Johannes F. Morgenbesser, Wolfgang Steiner, and Jörg Thuswaldner, Patterns in rational base number systems, arXiv:1203.4919 [math.NT], 2012. See p. 2.

Mathematica

a[n_] := a[n] = If[n == 0, 0, Module[{q, r}, {q, r} = QuotientRemainder[2*n, 3]; 10*a[q] + r]]; Array[a, 30, 0] (* Amiram Eldar, Apr 24 2025 *)

Crossrefs

Cf. A024629.

Sequence in context: A077249 A068070 A085953 * A225614 A303500 A037527

Adjacent sequences: A383343 A383344 A383345 * A383347 A383348 A383349

Keyword

nonn,base

Author

Michel Marcus, Apr 24 2025

Extensions

More terms from Amiram Eldar, Apr 24 2025

Status

approved