FASCINATING FACTORIALS

Introduction

How big is the factorial

Number of Trailing Zeros in Factorials

Factorion, amicable factorion and magic factorion

Various Kinds of factorials like half, double, multi, hyper and super factorials

Factorial primes

Subfactorials

Squares and factorials

Product of factorials

Prime counting function and factorials

Triangular Numbers and factorials

Euler totient function and factorials

Arabian Nights factorial

Some Interesting Observations

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References:

[1] George D. Poole, Integers and the sum of the factorials of their digits, Mathematics Magazine, 44 (1971) 278 -279.

[2] Clifford A. Pickover,  A. "The Loneliness of the Factorions." Ch. 22 in Keys to Infinity. New York: W. H. Freeman, pp. 169-171 and 319-320, 1995.

[3] C. Caldwell and G. L. Honaker, Jr., Is pi(6521)=6!+5!+2!+1! unique?, Math. Spectrum, 22:2 (2000/2001) 34-36.

[4] Gupta, Shyam Sunder "Sum of the factorials of the digits of integers" The Mathematical Gazette, 88(July 2004), pp.258-261.

[5] Abbott, Steve "SFD chains and factorion cycles" The Mathematical Gazette, 88(July 2004), pp.261-263.

[6] Guy, R. K. "Primes connected with factorials." A2 in Unsolved Problems in Number Theory, 3rd ed. New York: Springer-Verlag, pp. 10-11, 2004.

[7] Guy, R. K. "Equal product of factorials." B23 in Unsolved Problems in Number Theory, 3rd ed. New York: Springer-Verlag, pp. 123, 2004.

[8] Madachy, J. S. Madachy's Mathematical Recreations. New York: Dover, p. 167, 1979.

[9] Gardner Martin, "Factorial Oddities." Ch. 4 in Mathematical Magic Show: More Puzzles, Games, Diversions, Illusions and Other Mathematical Sleight-of-Mind from Scientific American. New York: Vintage, pp. 61 and 64, 1978.

[10] Pickover, Clifford A. "1001 Scheherazades " Ch. 75 in Wonders of Numbers: Adventures in Mathematics, Mind, and Meaning. Oxford, England: Oxford University Press, pp. 182-183 and 339, 2001.

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

[12] Sloane, N. J. A. Sequences A000142, A027868 , A014080,A214285,A188284, A006882, A000165, A001147, A007661, A002109, A000178, A055462, A088054, A002981, A002982, A007749, A080778, A084438, A037083, A000166, A014597, A025494, A049529, A066457, A115647, A101697, and A228311, in "The On-Line Encyclopedia of Integer Sequences."



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