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A018248 The 10-adic integer x = ...1787109376 satisfies x^2 = x. 24
6, 7, 3, 9, 0, 1, 7, 8, 7, 1, 8, 0, 0, 4, 7, 3, 4, 7, 7, 0, 6, 2, 2, 0, 0, 8, 3, 3, 9, 8, 5, 9, 9, 0, 9, 8, 3, 0, 1, 9, 6, 7, 6, 7, 5, 6, 7, 5, 2, 4, 4, 9, 9, 9, 8, 8, 1, 6, 3, 1, 9, 1, 4, 0, 9, 4, 3, 3, 8, 7, 3, 9, 9, 0, 1, 0, 9, 4, 1, 6, 0, 7, 9, 1, 0, 3, 8, 1, 9, 8, 0, 8, 6, 2, 9, 9, 6, 4, 0, 6, 9, 0, 6, 3, 7, 5, 3, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

The 10-adic numbers a and b defined in A018247 and this sequence 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.

R. Cuculière, Jeux Mathématiques, in Pour la Science, No. 6 (1986), 10-15.

V. deGuerre and R. A. Fairbairn, Automorphic numbers, J. Rec. Math., 1 (No. 3, 1968), 173-179.

M. Kraitchik, Sphinx, 1935, p. 1.

A. M. Robert, A Course in p-adic Analysis, Springer, 2000; see pp. 63, 419.

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..9999 (terms 0..999 from Paul D. Hanna)

Anonymous, Automorphic numbers (2)

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 = r^4 where r=...1441224165530407839804103263499879186432 (A120817). x = 10-adic limit_{n->infty} 6^(5^n). - Paul D. Hanna, Jul 06 2006

EXAMPLE

x equals the limit of the (n+1) trailing digits of 6^(5^n):

6^(5^0)=(6), 6^(5^1)=77(76), 6^(5^2)=28430288029929701(376),...

x = ...9442576576769103890995893380022607743740081787109376.

MATHEMATICA

b = {6}; g[n_] := Block[{k = 0, c}, While[c = FromDigits[Prepend[b, k]]; Mod[c^2, 10^n] != c, k++ ]; b = Prepend[b, k]]; Do[ g[n], {n, 2, 105}]; Reverse[b]

PROG

(PARI) {a(n)=local(b=6, v=[]); for(k=1, n+1, b=b^5%10^k; v=concat(v, (10*b\10^k))); v[n+1]} \\ Paul D. Hanna, Jul 06 2006

(PARI) Vecrev(digits(lift(chinese(Mod(0, 2^100), Mod(1, 5^100))))) \\ Seiichi Manyama, Aug 07 2019

CROSSREFS

A016090 gives associated automorphic numbers.

Cf. A018247, A033819.

The difference between this sequence & A018247 is A075693 and their product is A075693.

Cf. A120817, A120818, A091664.

The six examples given by deGuerre and Fairbairn are A055620, A054869, A018247, A018248, A259468, A259469.

Sequence in context: A139350 A092560 A272875 * A146485 A049254 A144028

Adjacent sequences:  A018245 A018246 A018247 * A018249 A018250 A018251

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 October 15 23:54 EDT 2019. Contains 328038 sequences. (Running on oeis4.)