Sunic, Zoran Rational tree morphisms and transducer integer sequences: definition and examples. (English) Zbl 1165.11086 J. Integer Seq. 10, No. 4, Article 07.4.3, 26 p. (2007). In this interesting paper the author defines transducer integer sequences: these are sequences of integers generated by transducers, i.e., essentially by finite automata where the output depends on the final state attained and on each transition step taken during the computation. These sequences are related to, but different from automatic sequences. These transducers generate self-similar (semi-)groups of trees auto- or endomorphisms, relating them to the theory of self-similar groups, see [V. Nekrashevych, Self-similar groups. Mathematical Surveys and Monographs 117. Providence, RI: American Mathematical Society (AMS) (2005; Zbl 1087.20032)] also known as automata groups, see [R. I. Grigorchuk,V. V. Nekrashevich and V. I. Sushchanskii, Automata, dynamical systems, and groups. Proc. Steklov Inst. Math. 231, 128–203 (2000); translation from Tr. Mat. Inst. Steklova 231, 134–214 (2000; Zbl 1155.37311)] or state-closed groups, see [M. V. Volkov, Izv. Ural. Gos. Univ. 22, Mat. Mekh. 4, 43–61 (2002; Zbl 1069.20054)], which is a field both very active and connected to numerous other fields, as shown by the bibliography of the paper under review. Reviewer: Jean-Paul Allouche (Orsay) MSC: 11Y55 Calculation of integer sequences 11B85 Automata sequences 20M20 Semigroups of transformations, relations, partitions, etc. 20M35 Semigroups in automata theory, linguistics, etc. Keywords:transducers; integer sequences; automatic sequences; self-similar groups; self-similar semigroups; tower of Hanoi problem Citations:Zbl 1087.20032; Zbl 1069.20054; Zbl 1155.37311 Software:OEIS PDFBibTeX XMLCite \textit{Z. Sunic}, J. Integer Seq. 10, No. 4, Article 07.4.3, 26 p. (2007; Zbl 1165.11086) Full Text: arXiv EuDML EMIS Online Encyclopedia of Integer Sequences: Nearest integer to 24*(2^n - 1)/n. Numbers whose base-3 representation contains no 2. Highest power of 3 dividing n. Tower of Hanoi positions (A055662) converted from base 3 to base 10. a(n)=p+q, where n=p-q and p, q, p+q are in A005836 (integers written without 2 in base 3). Numbers in ternary reflected Gray code order. Configuration of discs on pegs after n steps of the optimal solution to the Towers of Hanoi problem moving an odd number of discs from peg 0 to peg 2, or an even number from peg 0 to peg 1.