login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual Appeal: Today, Nov 11 2014, is the 4th anniversary of the launch of the new OEIS web site. 70,000 sequences have been added in these four years, all edited by volunteers. Please make a donation (tax deductible in the US) to help keep the OEIS running.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A018247 The 10-adic integer x = ...8212890625 satisfying x^2 = x. 18
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

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.

REFERENCES

W. W. R. Ball, Mathematical Recreations & Essays, N.Y. Macmillan Co, 1947.

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 = 10-adic 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.

The difference between A018248 & this sequence is A075693 and their product is A075693.

Sequence in context: A248260 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. Comments from Michael Somos.

Edited by David W. Wilson, Sep 26, 2002

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement .

Last modified December 18 00:20 EST 2014. Contains 252040 sequences.