December 1, 2025Open Access

Integers represented by binary recursive sequences

Puntos clave

Upper bounds on the largest index of a zero term were established, highlighting significant findings in integer sequences.
The growth order of absolute values was determined in relation to initial values, showcasing new features of these sequences.
This analysis extends previous work on Lucas sequences, emphasizing novel mathematical properties and bounds.
The findings suggest further exploration of recursive relations to enhance understanding of sequence behaviors.

Resumen

Abstract This paper is the continuation of Hajdu and Tijdeman (Ramanujan J 66:Article 74, 2025), where we deal with Lucas sequences. Here we study integers represented by integer sequences which satisfy binary recursive relations. In the case of non-degenerate sequences we give an upper bound on the largest index of a zero term and bounds on the growth order of the absolute values of the terms, both only in terms of the two initial values, which is a novel feature. Some of these bounds are best possible apart from a multiplicative constant.

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