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

3, 43, 143, 7143, 57143, 857143, 2857143, 42857143, 142857143, 7142857143, 57142857143, 857142857143, 2857142857143, 42857142857143, 142857142857143, 7142857142857143, 57142857142857143, 857142857142857143, 2857142857142857143, 42857142857142857143

Offset

1,1

Comments

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

Links

Eric M. Schmidt, Table of n, a(n) for n = 1..1000

Eric Weisstein's World of Mathematics, Automorphic Number.

Index entries for sequences related to automorphic numbers.

Index entries for sequences related to final digits of numbers.

Index entries for linear recurrences with constant coefficients, signature (11,-10,-1000,11000,-10000).

Formula

From Elmo R. Oliveira, Apr 12 2026: (Start)

a(n) = 11*a(n-1) - 10*a(n-2) - 1000*a(n-3) + 11000*a(n-4) - 10000*a(n-5) for n > 5.

G.f.: x * (3+10*x-300*x^2+9000*x^3-10000*x^4) / ((1-x) * (1-10*x) * (1+1000*x^3)). (End)

Mathematica

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

Prog

(SageMath) [inverse_mod(7, 10^n) for n in range(1, 1001)] # Eric M. Schmidt, Aug 18 2012

Crossrefs

Sequence in context: A003525 A042661 A281503 * A306970 A376737 A054698

Adjacent sequences: A030987 A030988 A030989 * A030991 A030992 A030993

Keyword

nonn,base,easy

Author

Eric W. Weisstein

Status

approved