

A018247


The 10adic integer x = ...8212890625 satisfying x^2 = x.


23



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

0,1


COMMENTS

The 10adic numbers a and b defined in this sequence and A018248 satisfy a^2=a, b^2=b, a+b=1, ab=0.  Michael Somos


REFERENCES

W. W. R. Ball, Mathematical Recreations & Essays, N.Y. Macmillan Co, 1947.
V. deGuerre and R. A. Fairbairn, Automorphic numbers, J. Rec. Math., 1 (No. 3, 1968), 173179.
M. Kraitchik, Sphinx, 1935, p. 1.


LINKS

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


FORMULA

x = 10adic limit_{n>infty} 5^(2^n) mod 10^(n+1).  Paul D. Hanna, Jul 08 2006


EXAMPLE

x = ...0863811000557423423230896109004106619977392256259918212890625.


MATHEMATICA

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]


PROG

(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


CROSSREFS

A007185 gives associated automorphic numbers.
Cf. A018248, A033819, A003226.
The difference between A018248 & this sequence is A075693 and their product is A075693.
The six examples given by deGuerre and Fairbairn are A055620, A054869, A018247, A018248, A259468, A259469.
Sequence in context: A253384 A175557 A217702 * A152025 A021099 A021023
Adjacent sequences: A018244 A018245 A018246 * A018248 A018249 A018250


KEYWORD

base,nonn


AUTHOR

Yoshihide Tamori (yo(AT)salk.edu)


EXTENSIONS

More terms from David W. Wilson
Edited by David W. Wilson, Sep 26 2002


STATUS

approved



