Abstract
Let (T_{n})_{nge 0} be the sequence of Tribonacci numbers defined by T_0=0 , T_1=T_2=1, and T_{n+3}= T_{n+2}+T_{n+1} +T_n for all nge 0 . In this note, we use of lower bounds for linear forms in logarithms of algebraic numbers and the Baker-Davenport reduction procedure to find all Tribonacci numbers that are concatenations of two repdigits.
Highlights
A repdigit is a positive integer R that has only one distinct digit when written in its decimal expansion
We study the problem of finding all Tribonacci numbers that are concatenations of two repdigits
Fn+2 = Fn+1 + Fn for all n ≥ 0, and (Bn)n≥0 be the sequence of balancing numbers given by B0 = 0, B1 = 1, and Bn+2 = 6Bn+1 − Bn for all n ≥ 0
Summary
A repdigit is a positive integer R that has only one distinct digit when written in its decimal expansion. For some positive integers d, with ≥ 1 and 0 ≤ d ≤ 9. The sequence of repdigits is sequence A010785 on the On-Line Encyclopedia of Integer Sequences (OEIS) [8]. The sequence of Tribonacci numbers is sequence A000073 on the OEIS. The first few terms of this sequence are given by (Tn)n≥0 = {0, 1, 1, 2, 4, 7, 13, 24, 44, 81, 149, 274, 504, 927, 1705, 3136, · · · }
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