Journal of Integer Sequences, Vol. 25 (2022), Article 22.8.7

Arithmetic Progressions of b-Prodigious Numbers

Michael Gohn
Dept. of Mathematics and Computer Sci.
DeSales University
2755 Station Ave.
Center Valley, PA 18034

Joshua Harrington
Department of Mathematics
Cedar Crest College
100 College Dr.
Allentown, PA 18104

Sophia Lebiere
Department of Mathematics
Tufts University
419 Boston Ave.
Medford, MA 02155

Hani Samamah
Department of Mathematics
University of Florida
Gainesville, FL 32611

Kyla Shappell
Department of Mathematics
Spring Hill College
4000 Dauphin St.
Mobile, AL 36608

Tony W. H. Wong
Department of Mathematics
Kutztown University of Pennsylvania
15200 Kutztown Road
Kutztown, PA 19530


A positive integer n is called a b-prodigious number if n is divisible by the product of its non-zero base-b digits. In this article, we investigate the maximum length of an arithmetic progression of b-prodigious numbers and the maximal length of consecutive sequences of b-prodigious numbers.

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(Concerned with sequence A055471.)

Received June 16 2022; revised version received October 18 2022. Published in Journal of Integer Sequences, October 25 2022.

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