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A030990 7-automorphic numbers ending in 3: final digits of 7n^2 agree with n. 1


%S 3,43,143,7143,57143,857143,2857143,42857143,142857143,7142857143,

%T 57142857143,857142857143,2857142857143,42857142857143,

%U 142857142857143,7142857142857143,57142857142857143

%N 7-automorphic numbers ending in 3: final digits of 7n^2 agree with n.

%C a(n) is the unique positive integer less than 10^n such that 7a(n) - 1 is divisible by 10^n. - _Eric M. Schmidt_, Aug 18 2012

%H Eric M. Schmidt, <a href="/A030990/b030990.txt">Table of n, a(n) for n = 1..1000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/AutomorphicNumber.html">Automorphic Number</a>

%H <a href="/index/Ar#automorphic">Index entries for sequences related to automorphic numbers</a>

%H <a href="/index/Fi#final">Index entries for sequences related to final digits of numbers</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (11,-10,-1000,11000,-10000).

%t LinearRecurrence[{11,-10,-1000,11000,-10000},{3,43,143,7143,57143},20] (* _Harvey P. Dale_, Apr 02 2018 *)

%o (Sage) [inverse_mod(7, 10^n) for n in range(1, 1001)] # _Eric M. Schmidt_, Aug 18 2012

%K nonn,base,changed

%O 1,1

%A _Eric W. Weisstein_

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Last modified December 8 12:07 EST 2019. Contains 329862 sequences. (Running on oeis4.)