Search: id:A007185
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%I A007185 M3940
%S A007185 5,25,625,625,90625,890625,2890625,12890625,212890625,8212890625,
%T A007185 18212890625,918212890625,9918212890625,59918212890625,259918212890625,
%U A007185 6259918212890625,56259918212890625,256259918212890625
%N A007185 Automorphic numbers ending in digit 5.
%C A007185 a(n)^2 == a(n) (mod 10^n), that is, a(n) is idempotent of Z[10^n].
%D A007185 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A007185 V. deGuerre and R. A. Fairbairn, Automorphic numbers, J. Rec. Math., 
               1 (No. 3, 1968), 173-179.
%D A007185 R. A. Fairbairn, More on automorphic numbers, J. Rec. Math., 2 (No. 3, 
               1969), 170-174.
%D A007185 Jan Gullberg, Mathematics, From the Birth of Numbers, W. W. Norton & 
               Co., NY, page 253-4.
%D A007185 Ya. I. Perelman, Algebra can be fun, pp. 97-98.
%D A007185 C. P. Schut, Idempotents. Report AM-R9101, Centrum voor Wiskunde en Informatica, 
               Amsterdam, 1991.
%D A007185 Xiaolong Ron Yu, Curious Numbers, Pi Mu Epsilon Journal, Spring 1999, 
               pp. 819-823.
%H A007185 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               AutomorphicNumber.html">Link to a section of The World of Mathematics.</
               a>
%H A007185 <a href="Sindx_Ar.html#automorphic">Index entries for sequences related 
               to automorphic numbers</a>
%F A007185 a(n) = 5^(2^n) mod 10^n.
%e A007185 a(5) = 90625 because 90625^2 == 8212890625 ends in 90625.
%Y A007185 A018247 gives associated 10-adic number.
%Y A007185 A003226 = {0, 1} union (this sequence) union A016090.
%Y A007185 Sequence in context: A082026 A101392 A078260 this_sequence A030995 A067270 
               A137114
%Y A007185 Adjacent sequences: A007182 A007183 A007184 this_sequence A007186 A007187 
               A007188
%K A007185 nonn,base
%O A007185 1,1
%A A007185 N. J. A. Sloane (njas(AT)research.att.com).
%E A007185 More terms from David W. Wilson (davidwwilson(AT)comcast.net)
%E A007185 Edited by David W. Wilson, Sep 26, 2002

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