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A018247 The 10-adic 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 (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. - 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), 173-179

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), 173-179

MathOverflow, Distribution of digits of pq-adic idempotents (aka “automorphic numbers”), 2014.

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

(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

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Last modified December 1 05:52 EST 2020. Contains 338833 sequences. (Running on oeis4.)