SMITH NUMBERS

Introduction

Various Kinds of Smith Numbers

Consecutive Smith Numbers

k-Smith Numbers

k-1 -Smith Numbers

Construction of Smith Numbers

Distribution of Smith Numbers v/s Primes

Highly Decomposable Smith Numbers

Some Interesting Observations

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References:

[1] Costello, Patrick. "A New Largest Smith Number," Fibonacci Quarterly, vol 40(4), 2002, pp. 369-371.

[2] Costello, Patrick and Lewis, Kathy. "Lots of Smiths," Mathematics Magazine, vol 75(3), 2002, pp. 223-226.

[3] Dudley,U. , "Smith Numbers", Mathematics Magazine, 67(1994),pp.62-65.

[4] Gupta, Shyam Sunder "Smith Numbers" Mathematical Spectrum ,37(2004/5), pp.27-29.

[5] Guy, R. K. "Smith Numbers." B49 in Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, pp. 103-104, 1994.

[6] Hoffman, P. The Man Who Loved Only Numbers: The Story of Paul Erdos and the Search for Mathematical Truth. New York: Hyperion, pp. 205-206, 1998.

[7] McDaniel,W.L., "Palindromic Smith numbers", Journal of Recreational Mathematics, 19(1987), pp. 34-37.

[8] McDaniel,W.L., "The Existence of infinitely Many k- Smith numbers", Fibonacci Quarterly, 25(1987), pp.76-80.

[9] McDaniel,W.L., "Powerful k-Smith Numbers", Fibonacci Quarterly, 25(1987), pp.225-228.

[10] McDaniel,W.L. and Yates, Samuel, "The Sum of Digits Function and its Application to A Generalization of the Smith Number Problem", Nieuw Archief Voor Wiskunde, 7, No, 1-2, March/July, (1989), 39-51.

[11] McDaniel,W.L., "On the Intersection of the Sets of Base b Smith Numbers and Niven Numbers", Missouri J. of Math. Sci. 2 (1990), 132-136.

[12] Oltikar, Sham and Keith Wayland. "Construction of Smith Number," Mathematics Magazine, vol 56(1), 1983,
pp. 36-37.

[13] Pickover, Clifford A. "A Brief History of Smith Numbers." Ch. 104 in Wonders of Numbers: Adventures in Mathematics, Mind, and Meaning. Oxford, England: Oxford University Press, pp. 247-248, 2001.

[14] Sloane, N. J. A. and Plouffe, S. The Encyclopedia of Integer Sequences. San Diego, CA: Academic Press, 1995.

[15] Sloane, N. J. A. Sequences A006753, A033662, A033663, A050218, A050224, A050225, A059754, A063844, A098834, A098835, A098836, A098837, A098838, A098839, A098840, A103123, A103124, A103125, A103126, A104166, A104167, A104168, A104169, A104170, A104171, A104390 and A104391, in "The On-Line Encyclopedia of Integer Sequences."

[16] Wells, David. The Penguin Dictionary of Curious and Interesting Numbers. Middlesex, England: Penguin Books, 1997.

[17] Wilansky, A. "Smith numbers",Two-Year College Mathematics Journal, 13(1982),p.21.

[18] Yates,S., "Smith numbers congruent to 4 (mod 9)", Journal of Recreational Mathematics, 19(1987), pp.139-141.



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