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Remarks on a Sequence of Minimal Niven Numbers

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Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 4893))

Abstract

In this short note we introduce two new sequences defined using the sum of digits in the representation of an integer in a certain base. A connection to Niven numbers is proposed and some results are proven.

Work by F. L. was done in the Spring of 2007 while he visited the Naval Postgraduate School. He would like to thank this institution for its hospitality. H. F. acknowledges support from the National Security Agency under contract RMA54. Research of P. S. was supported in part by a RIP grant from Naval Postgraduate School.

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References

  1. Cai, T.: On 2-Niven numbers and 3-Niven numbers. Fibonacci Quart. 34, 118–120 (1996)

    MATH  MathSciNet  Google Scholar 

  2. Cooper, C.N., Kennedy, R.E.: On consecutive Niven numbers. Fibonacci Quart. 21, 146–151 (1993)

    MathSciNet  Google Scholar 

  3. De Koninck, J.M., Doyon, N.: On the number of Niven numbers up to x. Fibonacci Quart. 41(5), 431–440 (2003)

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  4. De Koninck, J.M., Doyon, N., Katai, I.: On the counting function for the Niven numbers. Acta Arith. 106, 265–275 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  5. Grundman, H.G.: Sequences of consecutive Niven numbers. Fibonacci Quart. 32, 174–175 (1994)

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  6. Fredricksen, H., Ionascu, E.J., Luca, F., Stanica, P.: Minimal Niven numbers (I), submitted (2007)

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  7. Mauduit, C., Pomerance, C., Sárközy, A.: On the distribution in residue classes of integers with a fixed digit sum. The Ramanujan J. 9, 45–62 (2005)

    Article  MATH  Google Scholar 

  8. Mauduit, C., Sárközy, A.: On the arithmetic structure of integers whose sum of digits is fixed. Acta Arith. 81, 145–173 (1997)

    MATH  MathSciNet  Google Scholar 

  9. Rosen, K.H.: Elementary Number Theory, 5th edn. (2005)

    Google Scholar 

  10. Vardi, I.: Niven numbers. Computational Recreations in Mathematics, 19, 28–31 (1991)

    Google Scholar 

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Solomon W. Golomb Guang Gong Tor Helleseth Hong-Yeop Song

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© 2007 Springer-Verlag Berlin Heidelberg

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Fredricksen, H., Ionascu, E.J., Luca, F., Stănică, P. (2007). Remarks on a Sequence of Minimal Niven Numbers. In: Golomb, S.W., Gong, G., Helleseth, T., Song, HY. (eds) Sequences, Subsequences, and Consequences. Lecture Notes in Computer Science, vol 4893. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77404-4_16

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  • DOI: https://doi.org/10.1007/978-3-540-77404-4_16

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-77403-7

  • Online ISBN: 978-3-540-77404-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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