

A018247


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


34



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, Jnl. Rec. Math., 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?]
V. deGuerre and R. A. Fairbairn, Automorphic numbers, Jnl. Rec. Math., 1 (No. 3, 1968), 173179
MathOverflow, Distribution of digits of pqadic idempotents (aka “automorphic numbers”), 2014.
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
(PARI) Vecrev(digits(lift(chinese(Mod(1, 2^100), Mod(0, 5^100))))) \\ Seiichi Manyama, Aug 07 2019


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: A175557 A332455 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



