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A018247
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The 10-adic integer x = ...8212890625 satisfying x^2 = x.
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18
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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, 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, 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
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OFFSET
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0,1
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COMMENTS
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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.
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REFERENCES
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W. W. R. Ball, Mathematical Recreations & Essays, N.Y. Macmillan Co, 1947.
M. Kraitchik, Sphinx, 1935, p. 1.
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LINKS
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Eric M. Schmidt, Table of n, a(n) for n = 0..9999
Anonymous, Automorphic numbers (2) [broken link?]
Eric Weisstein's World of Mathematics, Automorphic numbers (1)
Index entries for sequences related to automorphic numbers
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FORMULA
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x = 10-adic limit_{n->infty} 5^(2^n) mod 10^(n+1). - Paul D. Hanna, Jul 08 2006
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EXAMPLE
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x = ...0863811000557423423230896109004106619977392256259918212890625.
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MATHEMATICA
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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]
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PROG
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(PARI) a(n)=local(t=5); for(k=1, n+1, t=t^2%10^k); t\10^n - Paul D. Hanna, Jul 08 2006
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CROSSREFS
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A007185 gives associated automorphic numbers.
Cf. A018248, A033819.
The difference between A018248 & this sequence is A075693 and their product is A075693.
Sequence in context: A197271 A175557 A217702 * A152025 A021099 A021023
Adjacent sequences: A018244 A018245 A018246 * A018248 A018249 A018250
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KEYWORD
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base,nonn
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AUTHOR
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Yoshihide Tamori (yo(AT)salk.edu).
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EXTENSIONS
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More terms from David W. Wilson. Comments from Michael Somos.
Edited by David W. Wilson, Sep 26, 2002
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STATUS
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approved
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