%I A018247
%S A018247 5,2,6,0,9,8,2,1,2,8,1,9,9,5,2,6,5,2,2,9,3,7,7,9,9,1,6,6,0,1,4,0,0,9,0,
               1,
%T A018247 6,9,8,0,3,2,3,2,4,3,2,4,7,5,5,0,0,0,1,1,8,3,6,8,0,8,5,9,0,5,6,6,1,2,6,
               0,
%U A018247 0,9,8,9,0,5,8,3,9,2,0,8,9,6,1,8,0,1,9,1,3,7,0,0,3,5,9,3,0,9,3,6,2,4,6,
               7
%N A018247 The 10-adic integer x = ...8212890625 satisfies x^2 = x.
%C A018247 The 10-adic numbers a and b defined in this sequence and A018248 satisfy 
               a^2=a, b^2=b, a+b=1, ab=0.
%D A018247 W. W. R. Ball, Mathematical Recreations & Essays, N.Y. Macmillan Co, 
               1947.
%D A018247 M. Kraitchik, Sphinx, 1935, p. 1.
%H A018247 Anonymous, <a href="http://freespace.virgin.net/anthony.edey/automorph.htm">
               Automorphic numbers (2)</a>
%H A018247 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               AutomorphicNumber.html">Automorphic numbers (1)</a>
%H A018247 <a href="Sindx_Ar.html#automorphic">Index entries for sequences related 
               to automorphic numbers</a>
%F A018247 x = 10-adic limit_{n->infty} 5^(2^n) mod 10^(n+1). - Paul D. Hanna (pauldhanna(AT)juno.com), 
               Jul 08 2006
%e A018247 x = ...0863811000557423423230896109004106619977392256259918212890625.
%t A018247 a = {5}; f[n_] := Block[{k = 0, c}, While[c = FromDigits[Prepend[a, k]]; 
               Mod[c^2, 10^n] != c, k++ ]; a = Prepend[a, k]]; Do[ f[n], {n, 2, 
               105}]; Reverse[a]
%o A018247 (PARI) a(n)=local(t=5);for(k=1,n+1,t=t^2%10^k);t\10^n - Paul D. Hanna 
               (pauldhanna(AT)juno.com), Jul 08 2006
%Y A018247 A007185 gives associated automorphic numbers.
%Y A018247 Cf. A018248, A033819.
%Y A018247 The difference between A018248 & this sequence is A075693 and their product 
               is A075693.
%Y A018247 Sequence in context: A071546 A154649 A100040 this_sequence A152025 A021099 
               A021023
%Y A018247 Adjacent sequences: A018244 A018245 A018246 this_sequence A018248 A018249 
               A018250
%K A018247 base,nonn
%O A018247 1,1
%A A018247 Yoshihide Tamori (yo(AT)salk.edu).
%E A018247 More terms from David W. Wilson (davidwwilson(AT)comcast.net). Comments 
               from Michael Somos.
%E A018247 Edited by David W. Wilson, Sep 26, 2002