1,1

Also called congruent numbers.

a(n)^2 == a(n) (mod 10^n), that is, a(n) is idempotent of Z[10^n].

R. Cuculiere, Jeux Mathematiques, 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.

R. A. Fairbairn, More on automorphic numbers, J. Rec. Math., 2 (No. 3, 1969), 170-174.

Jan Gullberg, Mathematics, From the Birth of Numbers, W. W. Norton & Co., NY, page 253-4.

Ya. I. Perelman, Algebra can be fun, pp. 97-98.

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

C. P. Schut, Idempotents. Report AM-R9101, Centrum voor Wiskunde en Informatica, Amsterdam, 1991.

Xiaolong Ron Yu, Curious Numbers, Pi Mu Epsilon Journal, Spring 1999, pp. 819-823.

Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.

Index entries for sequences related to automorphic numbers

a(n) = 16^(5^n) mod 10^n.

a(5) = 09376 because 09376^2 == 87909376 ends in 09376.

A018248 gives associated 10-adic number.

A003226 = {0, 1} union A007185 union (this sequence).

Sequence in context: A162863 A126462 A081066 this_sequence A137132 A053337 A155643

Adjacent sequences: A016087 A016088 A016089 this_sequence A016091 A016092 A016093

nonn,base

Robert G. Wilson v (rgwv(AT)rgwv.com), Dave Wilson (davidwwilson(AT)comcast.net)

Edited by David W. Wilson, Sep 26, 2002