A007185 - OEIS

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A007185

a(n) = 5^(2^n) mod 10^n.
(Formerly M3940)

5, 25, 625, 625, 90625, 890625, 2890625, 12890625, 212890625, 8212890625, 18212890625, 918212890625, 9918212890625, 59918212890625, 259918212890625, 6259918212890625, 56259918212890625, 256259918212890625 (list; graph; refs; listen; history; internal format)

	OFFSET	`1,1`
	COMMENTS	`Automorphic numbers ending in digit 5: a(n)^2 == a(n) (mod 10^n), that is, a(n) is an idempotent in Z[10^n].`
	REFERENCES	`V. deGuerre and R. A. Fairbairn, Automorphic numbers, J. Rec. Math., 1 (No. 3, 1968), 173-179.` `R. A. Fairbairn, More on automorphic numbers, J. Rec. Math., 2 (No. 3, 1969), 170-174.` `Jan Gullberg, Mathematics, From the Birth of Numbers, W. W. Norton & Co., NY, page 253-4.` `Ya. I. Perelman, Algebra can be fun, pp. 97-98.` `C. P. Schut, Idempotents. Report AM-R9101, Centrum voor Wiskunde en Informatica, Amsterdam, 1991.` `N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).` `Xiaolong Ron Yu, Curious Numbers, Pi Mu Epsilon Journal, Spring 1999, pp. 819-823.`
	LINKS	`Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.` `Index entries for sequences related to automorphic numbers`
	EXAMPLE	`a(5) = 90625 because 90625^2 == 8212890625 ends in 90625.`
	CROSSREFS	`A018247 gives the associated 10-adic number.` `A003226 = {0, 1} union (this sequence) union A016090.` `Sequence in context: A082026 A101392 A078260 * A175852 A030995 A067270` `Adjacent sequences: A007182 A007183 A007184 * A007186 A007187 A007188`
	KEYWORD	`nonn,base`
	AUTHOR	`N. J. A. Sloane (njas(AT)research.att.com).`
	EXTENSIONS	`More terms from David W. Wilson (davidwwilson(AT)comcast.net)` `Edited by David W. Wilson, Sep 26, 2002` `Further edited by N. J. A. Sloane (njas(AT)research.att.com), Jul 21 2010`

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Last modified February 12 21:29 EST 2012. Contains 205433 sequences.