Journal of Integer Sequences, Vol. 22 (2019), Article 19.6.3

Product of Consecutive Tribonacci Numbers With Only One Distinct Digit

Eric F. Bravo and Carlos A. Gómez
Department of Mathematics
Universidad del Valle
Calle 13 No 100 – 00

Florian Luca
School of Mathematics
University of the Witwatersrand
South Africa
Research Group in Algebraic Structures and Applications
King Abdulaziz University
Saudi Arabia
Department of Mathematics
University of Ostrava
30 Dubna 22, 701 03
Ostrava 1
Czech Republic


Let (Fn)n ≥ 0 be the sequence of Fibonacci numbers. Marques and Togbé proved that if the product Fn · · · Fn+l-1 is a repdigit (i.e., a number with only distinct digit in its decimal expansion), with at least two digits, then (l, n) = (1, 10). In this paper, we solve the same problem with Tribonacci numbers instead of Fibonacci numbers.

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(Concerned with sequences A010785 A101292.)

Received January 10 2019; revised versions received January 11 2019; August 14 2019. Published in Journal of Integer Sequences, August 24 2019.

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